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mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_sl.wikipedia.org&uselang=sl" class=""><span>Denarni prispevki</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Posebno:Registracija&returnto=Harshadovo+%C5%A1tevilo" title="Predlagamo vam, da si ustvarite račun in se prijavite, vendar to ni obvezno." class=""><span>Ustvari račun</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Posebno:Prijava&returnto=Harshadovo+%C5%A1tevilo" title="Prijava je zaželena, vendar ni obvezna [o]" 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class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Harshadovo število</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="P9jdi na članek v drugem jeziku. Na voljo v 27 jezikih." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-27" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">27 jezikov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D9%87%D8%B1%D8%B4%D8%AF" title="عدد هرشد – arabščina" lang="ar" hreflang="ar" data-title="عدد هرشد" data-language-autonym="العربية" data-language-local-name="arabščina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9B%D1%96%D0%BA%D1%96_%D1%85%D0%B0%D1%80%D1%88%D0%B0%D0%B4" title="Лікі харшад – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Лікі харшад" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Harshad-tal" title="Harshad-tal – danščina" lang="da" hreflang="da" data-title="Harshad-tal" data-language-autonym="Dansk" data-language-local-name="danščina" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Harshad-Zahl" title="Harshad-Zahl – nemščina" lang="de" hreflang="de" data-title="Harshad-Zahl" data-language-autonym="Deutsch" data-language-local-name="nemščina" 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/Harshad_number" title="Harshad number – angleščina" lang="en" hreflang="en" data-title="Harshad number" data-language-autonym="English" data-language-local-name="angleščina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_de_Harshad" title="Número de Harshad – španščina" lang="es" hreflang="es" data-title="Número de Harshad" data-language-autonym="Español" data-language-local-name="španščina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Harshad-luku" title="Harshad-luku – finščina" lang="fi" hreflang="fi" data-title="Harshad-luku" data-language-autonym="Suomi" data-language-local-name="finščina" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Nombre_harshad" title="Nombre harshad – francoščina" lang="fr" hreflang="fr" data-title="Nombre harshad" data-language-autonym="Français" data-language-local-name="francoščina" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%94%D7%A8%D7%A9%D7%90%D7%93" title="מספר הרשאד – hebrejščina" lang="he" hreflang="he" data-title="מספר הרשאד" data-language-autonym="עברית" data-language-local-name="hebrejščina" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Harshad-sz%C3%A1mok" title="Harshad-számok – madžarščina" lang="hu" hreflang="hu" data-title="Harshad-számok" data-language-autonym="Magyar" data-language-local-name="madžarščina" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D6%80%D5%B7%D5%A1%D5%A4%D5%AB_%D5%A9%D5%BE%D5%A5%D6%80" title="Հարշադի թվեր – armenščina" lang="hy" hreflang="hy" data-title="Հարշադի թվեր" data-language-autonym="Հայերեն" data-language-local-name="armenščina" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%80%D5%A1%D6%80%D5%B7%D5%A1%D5%BF_%D5%A9%D5%AB%D6%82%D5%A5%D6%80" title="Հարշատ թիւեր – Western Armenian" lang="hyw" hreflang="hyw" data-title="Հարշատ թիւեր" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_di_Harshad" title="Numero di Harshad – italijanščina" lang="it" hreflang="it" data-title="Numero di Harshad" data-language-autonym="Italiano" data-language-local-name="italijanščina" 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/%E3%83%8F%E3%83%BC%E3%82%B7%E3%83%A3%E3%83%83%E3%83%89%E6%95%B0" title="ハーシャッド数 – japonščina" lang="ja" hreflang="ja" data-title="ハーシャッド数" data-language-autonym="日本語" data-language-local-name="japonščina" 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/%ED%95%98%EC%83%A4%EB%93%9C_%EC%88%98" title="하샤드 수 – korejščina" lang="ko" hreflang="ko" data-title="하샤드 수" data-language-autonym="한국어" data-language-local-name="korejščina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B9%E0%A4%B0%E0%A5%8D%E0%A4%B7%E0%A4%A6_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="हर्षद संख्या – maratščina" lang="mr" hreflang="mr" data-title="हर्षद संख्या" data-language-autonym="मराठी" data-language-local-name="maratščina" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Harshadgetal" title="Harshadgetal – nizozemščina" lang="nl" hreflang="nl" data-title="Harshadgetal" data-language-autonym="Nederlands" data-language-local-name="nizozemščina" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczby_Nivena" title="Liczby Nivena – poljščina" lang="pl" hreflang="pl" data-title="Liczby Nivena" data-language-autonym="Polski" data-language-local-name="poljščina" 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/N%C3%BAmero_Harshad" title="Número Harshad – portugalščina" lang="pt" hreflang="pt" data-title="Número Harshad" data-language-autonym="Português" data-language-local-name="portugalščina" 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_harshad" title="Număr harshad – romunščina" lang="ro" hreflang="ro" data-title="Număr harshad" data-language-autonym="Română" data-language-local-name="romunščina" 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%A7%D0%B8%D1%81%D0%BB%D0%B0_%D1%85%D0%B0%D1%80%D1%88%D0%B0%D0%B4" title="Числа харшад – ruščina" lang="ru" hreflang="ru" data-title="Числа харшад" data-language-autonym="Русский" data-language-local-name="ruščina" 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/Harshad_number" title="Harshad number – Simple English" lang="en-simple" hreflang="en-simple" data-title="Harshad number" 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-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Harshadtal" title="Harshadtal – švedščina" lang="sv" hreflang="sv" data-title="Harshadtal" data-language-autonym="Svenska" data-language-local-name="švedščina" 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%B9%E0%AE%B0%E0%AF%8D%E0%AE%B7%E0%AE%A4%E0%AF%8D_%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="ஹர்ஷத் எண் – tamilščina" lang="ta" hreflang="ta" data-title="ஹர்ஷத் எண்" data-language-autonym="தமிழ்" data-language-local-name="tamilščina" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Harshad_say%C4%B1" title="Harshad sayı – turščina" lang="tr" hreflang="tr" data-title="Harshad sayı" data-language-autonym="Türkçe" data-language-local-name="turščina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%B0_%D1%85%D0%B0%D1%80%D1%88%D0%B0%D0%B4" title="Числа харшад – ukrajinščina" lang="uk" hreflang="uk" data-title="Числа харшад" data-language-autonym="Українська" data-language-local-name="ukrajinščina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%93%88%E6%B2%99%E5%BE%B7%E6%95%B8" title="哈沙德數 – kitajščina" lang="zh" hreflang="zh" data-title="哈沙德數" data-language-autonym="中文" data-language-local-name="kitajščina" class="interlanguage-link-target"><span>中文</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/Q375355#sitelinks-wikipedia" title="Uredi medjezikovne povezave" class="wbc-editpage">Uredi povezave</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="Imenski prostori"> <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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mw-list-item"><a href="/w/index.php?title=Harshadovo_%C5%A1tevilo&action=edit" title="Uredi izvorno kodo te strani [e]" accesskey="e"><span>Uredi kodo</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Harshadovo_%C5%A1tevilo&action=history" title="Prejšnje redakcije te strani [h]" accesskey="h"><span>Zgodovina</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Orodja strani"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Orodja" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Orodja</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Orodja</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Več možnosti" > <div class="vector-menu-heading"> Dejanja </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Harshadovo_%C5%A1tevilo"><span>Preberi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Harshadovo_%C5%A1tevilo&veaction=edit" title="Uredite to stran [v]" accesskey="v"><span>Uredi stran</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Harshadovo_%C5%A1tevilo&action=edit" title="Uredi izvorno kodo te strani [e]" accesskey="e"><span>Uredi kodo</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Harshadovo_%C5%A1tevilo&action=history"><span>Zgodovina</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Splošno </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:KajSePovezujeSem/Harshadovo_%C5%A1tevilo" title="Seznam vseh strani, ki se povezujejo sem [j]" accesskey="j"><span>Kaj se povezuje sem</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:RecentChangesLinked/Harshadovo_%C5%A1tevilo" rel="nofollow" title="Zadnje spremembe na straneh, s katerimi se povezuje ta stran [k]" accesskey="k"><span>Povezane spremembe</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:PosebneStrani" title="Seznam vseh posebnih strani [q]" accesskey="q"><span>Posebne strani</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Harshadovo_%C5%A1tevilo&oldid=6305552" title="Trajna povezava na to redakcijo strani"><span>Trajna povezava</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Harshadovo_%C5%A1tevilo&action=info" title="Več informacij o tej strani"><span>Podatki o strani</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Navedi&page=Harshadovo_%C5%A1tevilo&id=6305552&wpFormIdentifier=titleform" title="Informacije o tem, kako navajati to stran"><span>Navedba članka</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:UrlShortener&url=https%3A%2F%2Fsl.wikipedia.org%2Fwiki%2FHarshadovo_%25C5%25A1tevilo"><span>Pridobi skrajšani URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrCode&url=https%3A%2F%2Fsl.wikipedia.org%2Fwiki%2FHarshadovo_%25C5%25A1tevilo"><span>Prenesi kodo QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tiskanje/izvoz </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Posebno:Book&bookcmd=book_creator&referer=Harshadovo+%C5%A1tevilo"><span>Ustvari e-knjigo</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Harshadovo_%C5%A1tevilo&action=show-download-screen"><span>Prenesi kot PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Harshadovo_%C5%A1tevilo&printable=yes" title="Različica te strani za tisk [p]" accesskey="p"><span>Različica za tisk</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"> V drugih projektih </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/Q375355" title="Povezava na ustrezni predmet v podatkovni shrambi [g]" accesskey="g"><span>Predmet v Wikipodatkih</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="Orodja strani"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Videz"> <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">Videz</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skrij</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> <div id="siteSub" class="noprint">Iz Wikipedije, proste enciklopedije</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sl" dir="ltr"><p><b>Harshadovo število</b> je <a href="/wiki/Celo_%C5%A1tevilo" title="Celo število">celo</a> <a href="/wiki/%C5%A0tevilo" title="Število">število</a>, ki je <a href="/wiki/Deljenje" title="Deljenje">deljivo</a> z <a href="/wiki/Vsota" title="Vsota">vsoto</a> svojih <a href="/wiki/%C5%A0tevka" title="Števka">števk</a> v danem <a href="/wiki/%C5%A0tevilski_sistem" title="Številski sistem">številskem sestavu</a>. </p><p>Harshadovo število je <a href="/wiki/Definicija" title="Definicija">definiral</a> <a href="/wiki/Indijci" title="Indijci">indijski</a> <a href="/wiki/Matematik" class="mw-redirect" title="Matematik">matematik</a> <a href="/w/index.php?title=%C5%A0ri_Datatreja_Rama%C4%8Dandra_Kaprekar&action=edit&redlink=1" class="new" title="Šri Datatreja Ramačandra Kaprekar (stran ne obstaja)">Šri Datatreja Ramačandra Kaprekar</a>. Sama beseda <i>Harshad</i> izhaja iz <a href="/wiki/Sanskrit" class="mw-redirect" title="Sanskrit">sanskrita</a> in pomeni <i>veliko veselje</i>. </p><p>Gledano <a href="/wiki/Matematika" title="Matematika">matematično</a>, je <i>X</i> <a href="/wiki/Pozitivno_%C5%A1tevilo" title="Pozitivno število">pozitivno</a> celo število z <i>m</i> števkami, ki so zapisane v bazi <i>n</i> in števke so <i>a<sub>i</sub></i> (<i>i</i> = 0, 1, ..., <i>m</i> − 1). (<i>a<sub>i</sub></i> mora biti ali <a href="/wiki/0" title="0">nič</a> ali pa pozitivno celo število do <i>n</i>.) <i>X</i> je tako izražen kot </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 X=\sum _{i=0}^{m-1}a_{i}n^{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X=\sum _{i=0}^{m-1}a_{i}n^{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3fe2f63f6628c8b42c9821654d73e4f34cd7c95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.233ex; height:7.343ex;" alt="{\displaystyle X=\sum _{i=0}^{m-1}a_{i}n^{i}}"></span></dd></dl> <p>Če obstaja celo število <i>A</i>, tako da zgornja trditev drži, potem je <i>X</i> Harshadovo število v bazi <i>n</i>: </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 X=A\sum _{i=0}^{m-1}a_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>=</mo> <mi>A</mi> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X=A\sum _{i=0}^{m-1}a_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a246ec172acd96e6373c37c41e9ffea465940140" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.169ex; height:7.343ex;" alt="{\displaystyle X=A\sum _{i=0}^{m-1}a_{i}}"></span></dd></dl> <p>25 prvih Harshadovih števil z več kot eno števko v <a href="/wiki/Deseti%C5%A1ki_%C5%A1tevilski_sistem" title="Desetiški številski sistem">desetiškem številskem sistemu</a> so (<a href="/w/index.php?title=Spletna_enciklopedija_celo%C5%A1tevilskih_zaporedij&action=edit&redlink=1" class="new" title="Spletna enciklopedija celoštevilskih zaporedij (stran ne obstaja)">OEIS</a> <span class="nowrap external"><a href="//oeis.org/A005349" class="extiw" title="oeis:A005349">A005349</a></span>): </p> <dl><dd><a href="/wiki/10_(%C5%A1tevilo)" title="10 (število)">10</a>, <a href="/wiki/12_(%C5%A1tevilo)" title="12 (število)">12</a>, <a href="/wiki/18_(%C5%A1tevilo)" title="18 (število)">18</a>, <a href="/wiki/20_(%C5%A1tevilo)" title="20 (število)">20</a>, <a href="/wiki/21_(%C5%A1tevilo)" title="21 (število)">21</a>, <a href="/wiki/24_(%C5%A1tevilo)" title="24 (število)">24</a>, <a href="/wiki/27_(%C5%A1tevilo)" title="27 (število)">27</a>, <a href="/wiki/30_(%C5%A1tevilo)" title="30 (število)">30</a>, <a href="/wiki/36_(%C5%A1tevilo)" title="36 (število)">36</a>, <a href="/wiki/40_(%C5%A1tevilo)" title="40 (število)">40</a>, <a href="/wiki/42_(%C5%A1tevilo)" title="42 (število)">42</a>, <a href="/wiki/45_(%C5%A1tevilo)" title="45 (število)">45</a>, <a href="/wiki/48_(%C5%A1tevilo)" title="48 (število)">48</a>, <a href="/wiki/50_(%C5%A1tevilo)" title="50 (število)">50</a>, <a href="/wiki/54_(%C5%A1tevilo)" title="54 (število)">54</a>, <a href="/wiki/60_(%C5%A1tevilo)" title="60 (število)">60</a>, <a href="/wiki/63_(%C5%A1tevilo)" title="63 (število)">63</a>, <a href="/wiki/70_(%C5%A1tevilo)" title="70 (število)">70</a>, <a href="/wiki/72_(%C5%A1tevilo)" title="72 (število)">72</a>, <a href="/wiki/80_(%C5%A1tevilo)" title="80 (število)">80</a>, <a href="/wiki/81_(%C5%A1tevilo)" title="81 (število)">81</a>, <a href="/wiki/84_(%C5%A1tevilo)" title="84 (število)">84</a>, <a href="/wiki/90_(%C5%A1tevilo)" title="90 (število)">90</a>, <a href="/wiki/100_(%C5%A1tevilo)" title="100 (število)">100</a>, <a href="/wiki/102_(%C5%A1tevilo)" title="102 (število)">102</a>, <a href="/wiki/108_(%C5%A1tevilo)" title="108 (število)">108</a>, <a href="/wiki/110_(%C5%A1tevilo)" title="110 (število)">110</a>, <a href="/wiki/111_(%C5%A1tevilo)" title="111 (število)">111</a>, <a href="/wiki/112_(%C5%A1tevilo)" title="112 (število)">112</a>, <a href="/wiki/114_(%C5%A1tevilo)" title="114 (število)">114</a>, <a href="/wiki/117_(%C5%A1tevilo)" title="117 (število)">117</a>, <a href="/wiki/120_(%C5%A1tevilo)" title="120 (število)">120</a>, <a href="/wiki/126_(%C5%A1tevilo)" title="126 (število)">126</a>, <a href="/wiki/132_(%C5%A1tevilo)" title="132 (število)">132</a>, <a href="/wiki/133_(%C5%A1tevilo)" title="133 (število)">133</a>, <a href="/wiki/135_(%C5%A1tevilo)" title="135 (število)">135</a>, <a href="/wiki/140_(%C5%A1tevilo)" title="140 (število)">140</a>, <a href="/wiki/144_(%C5%A1tevilo)" title="144 (število)">144</a>, <a href="/wiki/150_(%C5%A1tevilo)" title="150 (število)">150</a>, <a href="/wiki/152_(%C5%A1tevilo)" title="152 (število)">152</a>, <a href="/wiki/153_(%C5%A1tevilo)" title="153 (število)">153</a>, <a href="/wiki/156_(%C5%A1tevilo)" title="156 (število)">156</a>, <a href="/wiki/162_(%C5%A1tevilo)" title="162 (število)">162</a>, <a href="/wiki/171_(%C5%A1tevilo)" title="171 (število)">171</a>, <a href="/wiki/180_(%C5%A1tevilo)" title="180 (število)">180</a>, <a href="/wiki/190_(%C5%A1tevilo)" title="190 (število)">190</a>, <a href="/wiki/192_(%C5%A1tevilo)" title="192 (število)">192</a>, <a href="/wiki/195_(%C5%A1tevilo)" title="195 (število)">195</a>, <a href="/wiki/198_(%C5%A1tevilo)" title="198 (število)">198</a>, <a href="/wiki/200_(%C5%A1tevilo)" title="200 (število)">200</a>, <a href="/wiki/201_(%C5%A1tevilo)" title="201 (število)">201</a></dd></dl> <p>Število, ki je Harshadovo število v vseh bazah, se imenuje vseharshadovo število. Obstajajo le štiri taka števila: <a href="/wiki/1_(%C5%A1tevilo)" title="1 (število)">1</a>, <a href="/wiki/2_(%C5%A1tevilo)" title="2 (število)">2</a>, <a href="/wiki/4_(%C5%A1tevilo)" title="4 (število)">4</a> in <a href="/wiki/6_(%C5%A1tevilo)" title="6 (število)">6</a>. </p> <style data-mw-deduplicate="TemplateStyles:r5570670">.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .asbox table{background:transparent}.mw-parser-output .asbox p{margin:0}.mw-parser-output .asbox p+p{margin-top:0.25em}.mw-parser-output .asbox-body{font-style:italic}.mw-parser-output .asbox-note{font-size:smaller}.mw-parser-output .asbox .navbar{position:absolute;top:-0.75em;right:1em;display:none}</style><div role="note" class="metadata plainlinks asbox stub"><table role="presentation"><tbody><tr class="noresize"><td><span typeof="mw:File"><a href="/wiki/Slika:E-to-the-i-pi.svg" class="mw-file-description"><img alt="Stub icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/34px-E-to-the-i-pi.svg.png" decoding="async" width="34" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/51px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td><td><p class="asbox-body">Ta matematični članek je <a href="/wiki/Wikipedija:%C5%A0krbina" title="Wikipedija:Škrbina">škrbina</a>. Pomagajte Wikipediji in ga <a class="external text" href="https://sl.wikipedia.org/w/index.php?title=Harshadovo_%C5%A1tevilo&action=edit">razširite</a>.</p></td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r5911192">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-prikaži"><a href="/wiki/Predloga:%C5%A0krbina-mat" title="Predloga:Škrbina-mat"><abbr title="Prikaži to predlogo">p</abbr></a></li><li class="nv-pogovor"><a href="/wiki/Pogovor_o_predlogi:%C5%A0krbina-mat" title="Pogovor o predlogi:Škrbina-mat"><abbr title="Pogovor o tej predlogi">p</abbr></a></li><li class="nv-uredi"><a class="external text" href="https://sl.wikipedia.org/w/index.php?title=Predloga:%C5%A0krbina-mat&action=edit"><abbr title="Uredi to predlogo">u</abbr></a></li></ul></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Pridobljeno iz »<a dir="ltr" href="https://sl.wikipedia.org/w/index.php?title=Harshadovo_število&oldid=6305552">https://sl.wikipedia.org/w/index.php?title=Harshadovo_število&oldid=6305552</a>«</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorija</a>: <ul><li><a href="/wiki/Kategorija:%C5%A0tevila" title="Kategorija:Števila">Števila</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skriti kategoriji: <ul><li><a href="/wiki/Kategorija:Vsi_%C5%A1krbinski_%C4%8Dlanki" title="Kategorija:Vsi škrbinski članki">Vsi škrbinski članki</a></li><li><a href="/wiki/Kategorija:Matemati%C4%8Dne_%C5%A1krbine" title="Kategorija:Matematične škrbine">Matematične škrbine</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Čas zadnje spremembe strani: 20:30, 27. september 2024.</li> <li id="footer-info-copyright">Besedilo se sme prosto uporabljati v skladu z dovoljenjem <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Priznanje avtorstva-Deljenje pod enakimi pogoji 4.0</a>; uveljavljajo se lahko dodatni pogoji. 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