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class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B5%D0%B7%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Безквадратно число – 保加利亚语" lang="bg" hreflang="bg" data-title="Безквадратно число" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Bez%C4%8Dtvercov%C3%A9_cel%C3%A9_%C4%8D%C3%ADslo" title="Bezčtvercové celé číslo – 捷克语" lang="cs" hreflang="cs" data-title="Bezčtvercové celé číslo" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Quadratfreie_Zahl" title="Quadratfreie Zahl – 德语" lang="de" hreflang="de" data-title="Quadratfreie Zahl" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Square-free_integer" title="Square-free integer – 英语" lang="en" hreflang="en" data-title="Square-free integer" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kvadrato-libera_entjero" title="Kvadrato-libera entjero – 世界语" lang="eo" hreflang="eo" data-title="Kvadrato-libera entjero" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Entero_libre_de_cuadrados" title="Entero libre de cuadrados – 西班牙语" lang="es" hreflang="es" data-title="Entero libre de cuadrados" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Entier_sans_facteur_carr%C3%A9" title="Entier sans facteur carré – 法语" lang="fr" hreflang="fr" data-title="Entier sans facteur carré" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Libre_de_cadrados" title="Libre de cadrados – 加利西亚语" lang="gl" hreflang="gl" data-title="Libre de cadrados" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/N%C3%A9gyzetmentes_sz%C3%A1m" title="Négyzetmentes szám – 匈牙利语" lang="hu" hreflang="hu" data-title="Négyzetmentes szám" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan_bulat_bebas_kuadrat" title="Bilangan bulat bebas kuadrat – 印度尼西亚语" lang="id" hreflang="id" data-title="Bilangan bulat bebas kuadrat" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Intero_privo_di_quadrati" title="Intero privo di quadrati – 意大利语" lang="it" hreflang="it" data-title="Intero privo di quadrati" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E3%82%92%E3%82%82%E3%81%9F%E3%81%AA%E3%81%84%E6%95%B4%E6%95%B0" title="平方因子をもたない整数 – 日语" lang="ja" hreflang="ja" data-title="平方因子をもたない整数" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%9C%EA%B3%B1_%EC%9D%B8%EC%88%98%EA%B0%80_%EC%97%86%EB%8A%94_%EC%A0%95%EC%88%98" title="제곱 인수가 없는 정수 – 韩语" lang="ko" hreflang="ko" data-title="제곱 인수가 없는 정수" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numerus_integer_quadratorum_privus" title="Numerus integer quadratorum privus – 拉丁语" lang="la" hreflang="la" data-title="Numerus integer quadratorum privus" data-language-autonym="Latina" data-language-local-name="拉丁语" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kwadraatvrij_geheel_getal" title="Kwadraatvrij geheel getal – 荷兰语" lang="nl" hreflang="nl" data-title="Kwadraatvrij geheel getal" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kvadratfritt_heltall" title="Kvadratfritt heltall – 书面挪威语" lang="nb" hreflang="nb" data-title="Kvadratfritt heltall" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczby_bezkwadratowe" title="Liczby bezkwadratowe – 波兰语" lang="pl" hreflang="pl" data-title="Liczby bezkwadratowe" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Inteiro_sem_fator_quadr%C3%A1tico" title="Inteiro sem fator quadrático – 葡萄牙语" lang="pt" hreflang="pt" data-title="Inteiro sem fator quadrático" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_liber_de_p%C4%83trate" title="Număr liber de pătrate – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Număr liber de pătrate" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%BE%D0%B5_%D0%BE%D1%82_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BE%D0%B2_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Свободное от квадратов число – 俄语" lang="ru" hreflang="ru" data-title="Свободное от квадратов число" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Square-free_integer" title="Square-free integer – Simple English" lang="en-simple" hreflang="en-simple" data-title="Square-free integer" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Deljivost_brez_kvadrata" title="Deljivost brez kvadrata – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Deljivost brez kvadrata" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%B8_%D0%B1%D1%80%D0%BE%D1%98" title="Бесквадратни број – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Бесквадратни број" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kvadratfritt_tal" title="Kvadratfritt tal – 瑞典语" lang="sv" hreflang="sv" data-title="Kvadratfritt tal" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%B0%E0%AF%8D%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%BE%E0%AE%B0%E0%AE%A3%E0%AE%BF%E0%AE%AF%E0%AE%B1%E0%AF%8D%E0%AE%B1_%E0%AE%AE%E0%AF%81%E0%AE%B4%E0%AF%81%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="வர்க்கக்காரணியற்ற முழுஎண் – 泰米尔语" lang="ta" hreflang="ta" data-title="வர்க்கக்காரணியற்ற முழுஎண்" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D1%96%D0%BB%D1%8C%D0%BD%D0%B5_%D0%B2%D1%96%D0%B4_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D1%96%D0%B2_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Вільне від квадратів число – 乌克兰语" lang="uk" hreflang="uk" data-title="Вільне від квадратів число" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%84%A1%E5%B9%B3%E6%96%B9%E6%95%B4%E6%95%B8" title="無平方整數 – 粤语" lang="yue" hreflang="yue" data-title="無平方整數" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q50706#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="命名空间"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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class="vector-dropdown-label-text">不转换</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-zh mw-list-item"><a href="/zh/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" lang="zh" hreflang="zh"><span>不转换</span></a></li><li id="ca-varlang-1" class="ca-variants-zh-Hans mw-list-item"><a href="/zh-hans/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" lang="zh-Hans" hreflang="zh-Hans"><span>简体</span></a></li><li id="ca-varlang-2" class="ca-variants-zh-Hant mw-list-item"><a href="/zh-hant/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" lang="zh-Hant" hreflang="zh-Hant"><span>繁體</span></a></li><li id="ca-varlang-3" class="ca-variants-zh-Hans-CN mw-list-item"><a href="/zh-cn/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" lang="zh-Hans-CN" hreflang="zh-Hans-CN"><span>大陆简体</span></a></li><li id="ca-varlang-4" class="ca-variants-zh-Hant-HK mw-list-item"><a href="/zh-hk/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" lang="zh-Hant-HK" hreflang="zh-Hant-HK"><span>香港繁體</span></a></li><li id="ca-varlang-5" class="ca-variants-zh-Hant-MO mw-list-item"><a href="/zh-mo/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" lang="zh-Hant-MO" hreflang="zh-Hant-MO"><span>澳門繁體</span></a></li><li id="ca-varlang-6" class="ca-variants-zh-Hans-MY mw-list-item"><a href="/zh-my/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" lang="zh-Hans-MY" hreflang="zh-Hans-MY"><span>大马简体</span></a></li><li id="ca-varlang-7" class="ca-variants-zh-Hans-SG mw-list-item"><a href="/zh-sg/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" lang="zh-Hans-SG" hreflang="zh-Hans-SG"><span>新加坡简体</span></a></li><li id="ca-varlang-8" class="ca-variants-zh-Hant-TW mw-list-item"><a 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href="/wiki/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0"><span>阅读</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&action=history"><span>查看历史</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 常规 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%85%A5%E9%A1%B5%E9%9D%A2/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" title="列出所有与本页相链的页面[j]" accesskey="j"><span>链入页面</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%87%BA%E6%9B%B4%E6%94%B9/%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" rel="nofollow" title="页面链出所有页面的更改[k]" accesskey="k"><span>相关更改</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Project:%E4%B8%8A%E4%BC%A0" title="上传图像或多媒体文件[u]" accesskey="u"><span>上传文件</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:%E7%89%B9%E6%AE%8A%E9%A1%B5%E9%9D%A2" title="全部特殊页面的列表[q]" accesskey="q"><span>特殊页面</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&oldid=73861539" title="此页面该修订版本的固定链接"><span>固定链接</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&action=info" title="关于此页面的更多信息"><span>页面信息</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:%E5%BC%95%E7%94%A8%E6%AD%A4%E9%A1%B5%E9%9D%A2&page=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&id=73861539&wpFormIdentifier=titleform" title="有关如何引用此页面的信息"><span>引用此页</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:URL%E7%BC%A9%E7%9F%AD%E7%A8%8B%E5%BA%8F&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E6%2597%25A0%25E5%25B9%25B3%25E6%2596%25B9%25E5%259B%25A0%25E5%25AD%2590%25E6%2595%25B0"><span>获取短链接</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E6%2597%25A0%25E5%25B9%25B3%25E6%2596%25B9%25E5%259B%25A0%25E5%25AD%2590%25E6%2595%25B0"><span>下载二维码</span></a></li> </ul> </div> </div> <div id="p-electronpdfservice-sidebar-portlet-heading" class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 打印/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&action=show-download-screen"><span>下载为PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p"><span>打印页面</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 在其他项目中 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q50706" title="链接到连接的数据仓库项目[g]" accesskey="g"><span>维基数据项目</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-noteTA-307af9e9" class="mw-indicator"><div class="mw-parser-output"><span class="skin-invert" typeof="mw:File"><span title="本页使用了标题或全文手工转换"><img alt="本页使用了标题或全文手工转换" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" 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.mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .ambox{border-left-color:#36c!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-night .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ambox{border-left-color:#36c!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-Expand plainlinks metadata ambox ambox-style" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/File:Antistub.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Antistub.svg/44px-Antistub.svg.png" decoding="async" width="44" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Antistub.svg/66px-Antistub.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Antistub.svg/88px-Antistub.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">此條目<b>需要擴充。</b><span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2013年2月14日</span>)</i></small><span class="hide-when-compact"><br /><small>请協助<a class="external text" href="https://zh.wikipedia.org/w/index.php?title=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&action=edit">改善这篇條目</a>，更進一步的信息可能會在<a href="/wiki/Talk:%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0" title="Talk:无平方因子数">討論頁</a>或<a href="/wiki/Wikipedia:%E6%89%A9%E5%85%85%E8%AF%B7%E6%B1%82" title="Wikipedia:扩充请求">扩充请求</a>中找到。请在擴充條目後將此模板移除。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <div id="noteTA-307af9e9" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Math"></div></div></div> <p><b>无平方因子数</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>（英語：<span lang="en">square-free integer</span>）是指其<a href="/wiki/%E5%9B%A0%E6%95%B8" title="因數">因數</a>中，沒有一個是<a href="/wiki/%E5%B9%B3%E6%96%B9%E6%95%B8" class="mw-redirect" title="平方數">平方數</a>的<a href="/wiki/%E6%AD%A3%E6%95%B4%E6%95%B8" class="mw-redirect" title="正整數">正整數</a>。簡言之，將一個這樣的數予以<a href="/wiki/%E6%95%B4%E6%95%B0%E5%88%86%E8%A7%A3" title="整数分解">質因數分解</a>後，所有<a href="/wiki/%E8%B3%AA%E5%9B%A0%E6%95%B8" title="質因數">質因數</a>的<a href="/wiki/%E5%86%AA" title="冪">冪</a>都不會大於或等於2。例如：<a href="/wiki/54" title="54">54</a>=<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0" /> </mrow> <annotation encoding="application/x-tex">{\displaystyle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:0; height:0.343ex;" alt="{\displaystyle }"></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\times 3^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>×</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\times 3^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/759ba9e1814ef8de3f372a7756046b549f14b686" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.22ex; height:2.676ex;" alt="{\displaystyle 2\times 3^{3}}"></span>，由於54有因數是平方數（<a href="/wiki/9" title="9"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3^{2}=9}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>9</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3^{2}=9}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ce3bb0717e9aa3fd7c54d6676a7a7fe15e78e66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.478ex; height:2.676ex;" alt="{\displaystyle 3^{2}=9}"></span></a>），所以54不是无平方因子数；而<a href="/wiki/55" title="55">55</a>=<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0" /> </mrow> <annotation encoding="application/x-tex">{\displaystyle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:0; height:0.343ex;" alt="{\displaystyle }"></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5\times 11}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>×</mo> <mn>11</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5\times 11}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f877a2893b76b50412153756fe3f4f4ac2ab5bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.328ex; height:2.176ex;" alt="{\displaystyle 5\times 11}"></span>，55沒有因數是平方數，所以55是无平方因子数。 </p><p>以數學概念說明：若一個數<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>是无平方因子数，則對於任意平方數<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b6401d5d0155afb1406770d1eb80badce4e08ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.576ex; height:2.676ex;" alt="{\displaystyle S^{2}}"></span>且<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S^{2}\leq R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>≤</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S^{2}\leq R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbd31980b3563155c1b59c6faf6ce516471e7be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.438ex; height:2.843ex;" alt="{\displaystyle S^{2}\leq R}"></span>則<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S^{2}\nmid R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>∤</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S^{2}\nmid R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e3eaa9752a01c929ccfa66b7a43d78af1a99d6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.277ex; height:3.176ex;" alt="{\displaystyle S^{2}\nmid R}"></span>；或者說當<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=P_{1}P_{2}P_{3}...P_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=P_{1}P_{2}P_{3}...P_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8aed32ea6ec014c3b8f926c0cb6aa5488d2ec9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.315ex; height:2.509ex;" alt="{\displaystyle R=P_{1}P_{2}P_{3}...P_{n}}"></span>且<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{1},P_{2},P_{3},...,P_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{1},P_{2},P_{3},...,P_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4b93335b90bf87e78c4845479bc76b212353865" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.588ex; height:2.509ex;" alt="{\displaystyle P_{1},P_{2},P_{3},...,P_{n}}"></span>皆為<a href="/wiki/%E8%B3%AA%E6%95%B8" class="mw-redirect" title="質數">質數</a>時，對於任意<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1\leq i,j\leq n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>≤</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>≤</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\leq i,j\leq n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a261efc4a9aa731385da988d0ccb68a202d522ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.549ex; height:2.509ex;" alt="{\displaystyle 1\leq i,j\leq n}"></span>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\neq j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>≠</mo> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\neq j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d95aeb406bb427ac96806bc00c30c91d31b858be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.859ex; height:2.676ex;" alt="{\displaystyle i\neq j}"></span>而言，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{i}\neq P_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>≠</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{i}\neq P_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f61b49c51529c54c926d8e64bab7bdc900bef83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.792ex; height:2.843ex;" alt="{\displaystyle P_{i}\neq P_{j}}"></span> </p><p>另一方面，<a href="/wiki/%E9%BB%98%E6%AF%94%E4%B9%8C%E6%96%AF%E5%87%BD%E6%95%B0" title="默比乌斯函数">默比乌斯函数</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu (n)\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu (n)\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f65917ca2e6c6d421a7be1d72cdf3cbae922b38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.867ex; height:2.843ex;" alt="{\displaystyle \mu (n)\neq 0}"></span>當且僅當<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8ce9ce38d06f6bf5a3fe063118c09c2b6202bfe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 1}"></span>且<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9ec7e1edc2e6d98f5aec2a39ae5f1c99d1e1425" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=1}"></span>或<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>為无平方因子数時 </p><p>前20個無平方因數的數是：<a href="/wiki/1" title="1">1</a>、<a href="/wiki/2" title="2">2</a>、<a href="/wiki/3" title="3">3</a>、<a href="/wiki/5" title="5">5</a>、<a href="/wiki/6" title="6">6</a>、<a href="/wiki/7" title="7">7</a>、<a href="/wiki/10" title="10">10</a>、<a href="/wiki/11" title="11">11</a>、<a href="/wiki/13" title="13">13</a>、<a href="/wiki/14" title="14">14</a>、<a href="/wiki/15" title="15">15</a>、<a href="/wiki/17" title="17">17</a>、<a href="/wiki/19" title="19">19</a>、<a href="/wiki/21" title="21">21</a>、<a href="/wiki/22" title="22">22</a>、<a href="/wiki/23" title="23">23</a>、<a href="/wiki/26" title="26">26</a>、<a href="/wiki/29" title="29">29</a>、<a href="/wiki/30" title="30">30</a>、<a href="/wiki/31" title="31">31</a>（<a href="/wiki/%E6%95%B4%E6%95%B8%E6%95%B8%E5%88%97%E7%B7%9A%E4%B8%8A%E5%A4%A7%E5%85%A8" title="整數數列線上大全">OEIS</a>數列<a href="//oeis.org/A005117" class="extiw" title="oeis:A005117">A005117</a>） </p><p>由於无平方因子数的所有質因數指數均為一次方，故除1以外，有關數的正因數數目必定是<a href="/wiki/2%E7%9A%84%E5%B9%82" title="2的幂">2的非負整數次方</a>。 </p><p>將无平方因子数分解為兩數之積，這兩數一定<a href="/wiki/%E4%BA%92%E8%B3%AA" title="互質">互質</a>。<sup class="noprint Inline-Template" style="white-space:nowrap;">[<a href="/wiki/Wikipedia:%E5%8F%AF%E4%BE%9B%E6%9F%A5%E8%AD%89" title="Wikipedia:可供查證"><span title="该标签附近的材料需要与引用的来源进行查证。">查证请求</span></a>]</sup><style data-mw-deduplicate="TemplateStyles:r83946278">.mw-parser-output .template-facttext{background-color:var(--background-color-neutral,#eaecf0);color:inherit;margin:-.3em 0;padding:.3em 0}</style><sup class="noprint Template-Fact"><a href="/wiki/Wikipedia:%E5%88%97%E6%98%8E%E6%9D%A5%E6%BA%90" title="Wikipedia:列明来源"><span style="white-space: nowrap;" title="来源请求。">[來源請求]</span></a></sup><sup class="noprint"><a href="/wiki/Wikipedia:%E9%9D%9E%E5%8E%9F%E5%88%9B%E7%A0%94%E7%A9%B6" title="Wikipedia:非原创研究"><span title="原创研究验证请求"><span style="white-space: nowrap;">[原創研究？]</span></span></a></sup> </p><p>依定義，顯然所有的<a href="/wiki/%E8%B3%AA%E6%95%B8" class="mw-redirect" title="質數">質數</a>、<a href="/wiki/%E6%A5%94%E5%BD%A2%E6%95%B0" title="楔形数">楔形数</a>、<a href="/wiki/%E8%B3%AA%E6%95%B8%E9%9A%8E%E4%B9%98" title="質數階乘">質數階乘</a>與有4個正因數的<a href="/wiki/%E5%8D%8A%E8%B3%AA%E6%95%B8" class="mw-redirect" title="半質數">半質數</a>都是无平方因子数。 </p> <div class="mw-heading mw-heading2"><h2 id="不含平方因子的数的分布"><span id=".E4.B8.8D.E5.90.AB.E5.B9.B3.E6.96.B9.E5.9B.A0.E5.AD.90.E7.9A.84.E6.95.B0.E7.9A.84.E5.88.86.E5.B8.83"></span>不含平方因子的数的分布</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&action=edit&section=1" title="编辑章节：不含平方因子的数的分布"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>如果用<i>Q</i>(<i>x</i>)来表示1和<i>x</i>之间的不含平方因子的数，则： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q(x)={\frac {6x}{\pi ^{2}}}+O({\sqrt {x}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi>x</mi> </mrow> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mi>O</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>x</mi> </msqrt> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q(x)={\frac {6x}{\pi ^{2}}}+O({\sqrt {x}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b3eedca12972f94aa54ac04770f8f3f4d0f6e63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:21.093ex; height:5.509ex;" alt="{\displaystyle Q(x)={\frac {6x}{\pi ^{2}}}+O({\sqrt {x}})}"></span></dd></dl> <p>因此，不含平方因子的数的<a href="/wiki/%E8%87%AA%E7%84%B6%E5%AF%86%E5%BA%A6" title="自然密度">自然密度</a>为： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{x\to \infty }{\frac {Q(x)}{x}}={\frac {6}{\pi ^{2}}}={\frac {1}{\zeta (2)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>6</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ζ</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to \infty }{\frac {Q(x)}{x}}={\frac {6}{\pi ^{2}}}={\frac {1}{\zeta (2)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9faa8937914b7f67359a992960b87d7bed62ec2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:24.752ex; height:6.509ex;" alt="{\displaystyle \lim _{x\to \infty }{\frac {Q(x)}{x}}={\frac {6}{\pi ^{2}}}={\frac {1}{\zeta (2)}}}"></span></dd></dl> <p>其中ζ是<a href="/wiki/%E9%BB%8E%E6%9B%BC%CE%B6%E5%87%BD%E6%95%B0" class="mw-redirect" title="黎曼ζ函数">黎曼ζ函数</a>。 </p><p>类似地，如果用<i>Q</i>(<i>x</i>,<i>n</i>)来表示1和<i>x</i>之间的不含<i>n</i>次方因子的数，则我们可以证明： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{x\to \infty }{\frac {Q(x,n)}{x}}={\frac {1}{\zeta (n)}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ζ</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to \infty }{\frac {Q(x,n)}{x}}={\frac {1}{\zeta (n)}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1f79865040e47990d8c30e6fd161bb227c5bc20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.736ex; height:6.509ex;" alt="{\displaystyle \lim _{x\to \infty }{\frac {Q(x,n)}{x}}={\frac {1}{\zeta (n)}}.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="參考文獻"><span id=".E5.8F.83.E8.80.83.E6.96.87.E7.8D.BB"></span>參考文獻</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&action=edit&section=2" title="编辑章节：參考文獻"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation book">张鸿林; 葛显良. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nduYtmyywcUC&source=gbs_navlinks_s">英汉数学词汇</a>. 清华大学出版社. 2005: <a rel="nofollow" class="external text" href="https://www.google.co.uk/books/edition/%E8%8B%B1%E6%B1%89%E6%95%B0%E5%AD%A6%E8%AF%8D%E6%B1%87/nduYtmyywcUC?hl=en&gbpv=1&pg=PA703&printsec=frontcover&dq=free">703</a>. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9787302098935" title="Special:网络书源/9787302098935"><span title="国际标准书号">ISBN</span> 9787302098935</a>. <q>square-free number 无平方因子数</q></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E5%B9%B3%E6%96%B9%E5%9B%A0%E5%AD%90%E6%95%B0&rft.au=%E5%BC%A0%E9%B8%BF%E6%9E%97&rft.au=%E8%91%9B%E6%98%BE%E8%89%AF&rft.btitle=%E8%8B%B1%E6%B1%89%E6%95%B0%E5%AD%A6%E8%AF%8D%E6%B1%87&rft.date=2005&rft.genre=book&rft.isbn=9787302098935&rft.pages=703&rft.pub=%E6%B8%85%E5%8D%8E%E5%A4%A7%E5%AD%A6%E5%87%BA%E7%89%88%E7%A4%BE&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DnduYtmyywcUC%26source%3Dgbs_navlinks_s&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r84265675">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output 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title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:Divisor_classes_navbox&action=edit&redlink=1" class="new" title="Template talk:Divisor classes navbox（页面不存在）"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:Divisor_classes_navbox" title="Special:编辑页面/Template:Divisor classes navbox"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="和因數有關的整數分類" style="font-size:110%;margin:0 5em">和因數有關的整數分類</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">簡介</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%95%B4%E6%95%B0%E5%88%86%E8%A7%A3" title="整数分解">質因數分解</a></li> <li><a href="/wiki/%E5%9B%A0%E6%95%B8" title="因數">因數</a></li> <li><a href="/wiki/%E5%85%83%E5%9B%A0%E6%95%B8" title="元因數">元因數</a></li> <li><a href="/wiki/%E9%99%A4%E6%95%B8%E5%87%BD%E6%95%B8" title="除數函數">除數函數</a></li> <li><a href="/wiki/%E8%B3%AA%E5%9B%A0%E6%95%B8" title="質因數">質因數</a></li> <li><a href="/wiki/%E7%AE%97%E6%9C%AF%E5%9F%BA%E6%9C%AC%E5%AE%9A%E7%90%86" title="算术基本定理">算术基本定理</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Lattice_of_the_divisibility_of_60.svg" class="mw-file-description" title="Divisibility of 60"><img alt="Divisibility of 60" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/200px-Lattice_of_the_divisibility_of_60.svg.png" decoding="async" width="200" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/300px-Lattice_of_the_divisibility_of_60.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/400px-Lattice_of_the_divisibility_of_60.svg.png 2x" data-file-width="313" data-file-height="250" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">依因數分解分類</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%B4%A8%E6%95%B0" title="质数">质数</a></li> <li><a href="/wiki/%E5%90%88%E6%95%B0" title="合数">合数</a></li> <li><a href="/wiki/%E5%8D%8A%E7%B4%A0%E6%95%B0" title="半素数">半素数</a></li> <li><a href="/wiki/%E6%99%AE%E6%B4%9B%E5%B0%BC%E5%85%8B%E6%95%B0" title="普洛尼克数">普洛尼克数</a></li> <li><a href="/wiki/%E6%A5%94%E5%BD%A2%E6%95%B0" title="楔形数">楔形数</a></li> <li><a class="mw-selflink selflink">无平方数因数的数</a></li> <li><a href="/wiki/%E5%86%AA%E6%95%B8" title="冪數">冪數</a></li> <li><a href="/wiki/%E8%B3%AA%E6%95%B8%E5%86%AA" title="質數冪">質數冪</a></li> <li><a href="/wiki/%E5%B9%B3%E6%96%B9%E6%95%B8" class="mw-redirect" title="平方數">平方數</a></li> <li><a href="/wiki/%E7%AB%8B%E6%96%B9%E6%95%B8" title="立方數">立方數</a></li> <li><a href="/wiki/%E6%AC%A1%E6%96%B9%E6%95%B8" title="次方數">次方數</a></li> <li><a href="/wiki/%E9%98%BF%E5%96%80%E7%90%89%E6%96%AF%E6%95%B8" title="阿喀琉斯數">阿喀琉斯數</a></li> <li><a href="/wiki/%E5%85%89%E6%BB%91%E6%95%B8" title="光滑數">光滑數</a></li> <li><a href="/wiki/%E6%AD%A3%E8%A7%84%E6%95%B0_(%E6%95%B4%E6%95%B0)" title="正规数 (整数)">正规数</a></li> <li><a href="/wiki/%E7%B2%97%E7%B3%99%E6%95%B8" title="粗糙數">粗糙數</a></li> <li><a href="/wiki/%E4%B8%8D%E5%B0%8B%E5%B8%B8%E6%95%B8" title="不尋常數">不尋常數</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">依因數和分類</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%AE%8C%E5%85%A8%E6%95%B0" title="完全数">完全数</a></li> <li><a href="/wiki/%E6%AE%86%E5%AE%8C%E5%85%A8%E6%95%B8" title="殆完全數">殆完全數</a></li> <li><a href="/wiki/%E5%87%86%E5%AE%8C%E5%85%A8%E6%95%B0" title="准完全数">准完全数</a></li> <li><a href="/wiki/%E5%A4%9A%E9%87%8D%E5%AE%8C%E5%85%A8%E6%95%B8" title="多重完全數">多重完全數</a></li> <li><a href="/wiki/Hemiperfect%E6%95%B8" title="Hemiperfect數">Hemiperfect數</a></li> <li><span class="ilh-all" data-orig-title="Hyperperfect number" data-lang-code="en" data-lang-name="英语" data-foreign-title="Hyperperfect number"><span class="ilh-page"><a href="/w/index.php?title=Hyperperfect_number&action=edit&redlink=1" class="new" title="Hyperperfect number（页面不存在）">Hyperperfect number</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Hyperperfect_number" class="extiw" title="en:Hyperperfect number"><span lang="en" dir="auto">Hyperperfect number</span></a></span>）</span></span></li> <li><a href="/wiki/%E8%B6%85%E5%AE%8C%E5%85%A8%E6%95%B8" title="超完全數">超完全數</a></li> <li><a href="/wiki/%E5%85%83%E5%AE%8C%E5%85%A8%E6%95%B8" title="元完全數">元完全數</a></li> <li><a href="/wiki/%E5%8D%8A%E5%AE%8C%E5%85%A8%E6%95%B0" title="半完全数">半完全数</a></li> <li><a href="/wiki/%E6%9C%AC%E5%8E%9F%E5%8D%8A%E5%AE%8C%E5%85%A8%E6%95%B0" title="本原半完全数">本原半完全数</a></li> <li><a href="/wiki/%E5%AF%A6%E9%9A%9B%E6%95%B8" title="實際數">實際數</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">有許多因數</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%BF%87%E5%89%A9%E6%95%B0" title="过剩数">过剩数</a></li> <li><a href="/wiki/%E6%9C%AC%E5%8E%9F%E9%81%8E%E5%89%A9%E6%95%B8" title="本原過剩數">本原過剩數</a></li> <li><a href="/wiki/%E9%AB%98%E9%81%8E%E5%89%A9%E6%95%B8" title="高過剩數">高過剩數</a></li> <li><a href="/wiki/%E8%B6%85%E9%81%8E%E5%89%A9%E6%95%B8" title="超過剩數">超過剩數</a></li> <li><a href="/wiki/%E5%8F%AF%E7%BE%85%E8%96%A9%E9%87%8C%E9%81%8E%E5%89%A9%E6%95%B8" title="可羅薩里過剩數">可羅薩里過剩數</a></li> <li><a href="/wiki/%E9%AB%98%E5%90%88%E6%88%90%E6%95%B0" title="高合成数">高合成数</a></li> <li><span class="ilh-all" data-orig-title="Superior highly composite number" data-lang-code="en" data-lang-name="英语" data-foreign-title="Superior highly composite number"><span class="ilh-page"><a href="/w/index.php?title=Superior_highly_composite_number&action=edit&redlink=1" class="new" title="Superior highly composite number（页面不存在）">Superior highly composite number</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Superior_highly_composite_number" class="extiw" title="en:Superior highly composite number"><span lang="en" dir="auto">Superior highly composite number</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%A5%87%E7%95%B0%E6%95%B8_(%E6%95%B8%E8%AB%96)" title="奇異數 (數論)">奇異數</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">和<a href="/wiki/%E7%9C%9F%E5%9B%A0%E5%AD%90%E5%92%8C%E6%95%B8%E5%88%97" title="真因子和數列">真因子和數列</a>有關</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%B8%8D%E5%8F%AF%E5%8F%8A%E6%95%B0" title="不可及数">不可及数</a></li> <li><a href="/wiki/%E7%9B%B8%E4%BA%B2%E6%95%B0" title="相亲数">相亲数</a></li> <li><a href="/wiki/%E7%9B%B8%E4%BA%B2%E6%95%B0%E9%93%BE" title="相亲数链">交際數</a></li> <li><a href="/wiki/%E5%A9%9A%E7%B4%84%E6%95%B8" title="婚約數">婚約數</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">其他</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%BA%8F%E6%95%B0" title="亏数">亏数</a></li> <li><a href="/wiki/%E5%8F%8B%E8%AA%BC%E6%95%B8" title="友誼數">友誼數</a></li> <li><a href="/wiki/%E5%8F%8B%E8%AA%BC%E6%95%B8" title="友誼數">孤獨數</a></li> <li><a href="/wiki/%E5%8D%93%E8%B6%8A%E6%95%B0" title="卓越数">卓越数</a></li> <li><a href="/wiki/%E6%AD%90%E7%88%BE%E8%AA%BF%E5%92%8C%E6%95%B8" title="歐爾調和數">歐爾調和數</a></li> <li><a href="/wiki/%E4%BD%A9%E6%9C%8D%E6%95%B8" title="佩服數">佩服數</a></li> <li><a href="/wiki/%E7%AF%80%E5%84%89%E6%95%B8" title="節儉數">節儉數</a></li> <li><a href="/wiki/%E7%AD%89%E6%95%B8%E4%BD%8D%E6%95%B8" title="等數位數">等數位數</a></li> <li><a href="/wiki/%E5%A5%A2%E4%BE%88%E6%95%B8" title="奢侈數">奢侈數</a></li></ul> </div></td></tr></tbody></table></div> <table class="metadata plainlinks stub" role="presentation" style="background:transparent"><tbody><tr class="noresize"><td><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics-p.svg" class="mw-file-description"><img alt="小作品圖示" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/30px-Nuvola_apps_edu_mathematics-p.svg.png" 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