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Disponible en 34 langues." > <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-34" 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">34 langues</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%86%D8%A7%D9%82%D8%B5" title="عدد ناقص – arabe" lang="ar" hreflang="ar" data-title="عدد ناقص" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Niver_diouerus" title="Niver diouerus – breton" lang="br" hreflang="br" data-title="Niver diouerus" data-language-autonym="Brezhoneg" data-language-local-name="breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_deficient" title="Nombre deficient – catalan" lang="ca" hreflang="ca" data-title="Nombre deficient" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Deficientn%C3%AD_%C4%8D%C3%ADslo" title="Deficientní číslo – tchèque" lang="cs" hreflang="cs" data-title="Deficientní číslo" data-language-autonym="Čeština" data-language-local-name="tchèque" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Defektivt_tal" title="Defektivt tal – danois" lang="da" hreflang="da" data-title="Defektivt tal" data-language-autonym="Dansk" data-language-local-name="danois" 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/Defiziente_Zahl" title="Defiziente Zahl – allemand" lang="de" hreflang="de" data-title="Defiziente Zahl" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BB%CE%BB%CE%B9%CF%80%CE%AE%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82" title="Ελλιπής αριθμός – grec" lang="el" hreflang="el" data-title="Ελλιπής αριθμός" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/N%C3%B9mer_difet%C3%ACv" title="Nùmer difetìv – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Nùmer difetìv" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Deficient_number" title="Deficient number – anglais" lang="en" hreflang="en" data-title="Deficient number" data-language-autonym="English" data-language-local-name="anglais" 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/Manka_nombro" title="Manka nombro – espéranto" lang="eo" hreflang="eo" data-title="Manka nombro" data-language-autonym="Esperanto" data-language-local-name="espéranto" 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/N%C3%BAmero_defectivo" title="Número defectivo – espagnol" lang="es" hreflang="es" data-title="Número defectivo" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki_defektibo" title="Zenbaki defektibo – basque" lang="eu" hreflang="eu" data-title="Zenbaki defektibo" data-language-autonym="Euskara" data-language-local-name="basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Vajaa_luku" title="Vajaa luku – finnois" lang="fi" hreflang="fi" data-title="Vajaa luku" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%BAmero_defectivo" title="Número defectivo – galicien" lang="gl" hreflang="gl" data-title="Número defectivo" data-language-autonym="Galego" data-language-local-name="galicien" class="interlanguage-link-target"><span>Galego</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%97%D7%A1%D7%A8" title="מספר חסר – hébreu" lang="he" hreflang="he" data-title="מספר חסר" data-language-autonym="עברית" data-language-local-name="hébreu" 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/Hi%C3%A1nyos_sz%C3%A1mok" title="Hiányos számok – hongrois" lang="hu" hreflang="hu" data-title="Hiányos számok" data-language-autonym="Magyar" data-language-local-name="hongrois" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_difettivo" title="Numero difettivo – italien" lang="it" hreflang="it" data-title="Numero difettivo" data-language-autonym="Italiano" data-language-local-name="italien" 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/%E4%B8%8D%E8%B6%B3%E6%95%B0" title="不足数 – japonais" lang="ja" hreflang="ja" data-title="不足数" data-language-autonym="日本語" data-language-local-name="japonais" 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/%EB%B6%80%EC%A1%B1%EC%88%98" title="부족수 – coréen" lang="ko" hreflang="ko" data-title="부족수" data-language-autonym="한국어" data-language-local-name="coréen" 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_defectivus" title="Numerus defectivus – latin" lang="la" hreflang="la" data-title="Numerus defectivus" data-language-autonym="Latina" data-language-local-name="latin" 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/Gebrekkig_getal" title="Gebrekkig getal – néerlandais" lang="nl" hreflang="nl" data-title="Gebrekkig getal" data-language-autonym="Nederlands" data-language-local-name="néerlandais" 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_deficytowe" title="Liczby deficytowe – polonais" lang="pl" hreflang="pl" data-title="Liczby deficytowe" data-language-autonym="Polski" data-language-local-name="polonais" 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_defectivo" title="Número defectivo – portugais" lang="pt" hreflang="pt" data-title="Número defectivo" data-language-autonym="Português" data-language-local-name="portugais" 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_deficient" title="Număr deficient – roumain" lang="ro" hreflang="ro" data-title="Număr deficient" data-language-autonym="Română" data-language-local-name="roumain" 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%9D%D0%B5%D0%B4%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%BE%D1%87%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Недостаточное число – russe" lang="ru" hreflang="ru" data-title="Недостаточное число" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/N%C3%B9mmuru_difittivu" title="Nùmmuru difittivu – sicilien" lang="scn" hreflang="scn" data-title="Nùmmuru difittivu" data-language-autonym="Sicilianu" data-language-local-name="sicilien" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Deficient_number" title="Deficient number – Simple English" lang="en-simple" hreflang="en-simple" data-title="Deficient 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Redundantn%C3%A9_%C4%8D%C3%ADslo" title="Redundantné číslo – slovaque" lang="sk" hreflang="sk" data-title="Redundantné číslo" data-language-autonym="Slovenčina" data-language-local-name="slovaque" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Nezadostno_%C5%A1tevilo" title="Nezadostno število – slovène" lang="sl" hreflang="sl" data-title="Nezadostno število" data-language-autonym="Slovenščina" data-language-local-name="slovène" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Defekt_tal" title="Defekt tal – suédois" lang="sv" hreflang="sv" data-title="Defekt tal" data-language-autonym="Svenska" data-language-local-name="suédois" 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%95%E0%AF%81%E0%AE%B1%E0%AF%88%E0%AE%B5%E0%AF%86%E0%AE%A3%E0%AF%8D_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="குறைவெண் (கணிதம்) – tamoul" lang="ta" hreflang="ta" data-title="குறைவெண் (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="tamoul" 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%9D%D0%B5%D0%B4%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%BD%D1%96_%D1%87%D0%B8%D1%81%D0%BB%D0%B0" title="Недостатні числа – ukrainien" lang="uk" hreflang="uk" data-title="Недостатні числа" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%86%D8%A7%D9%82%D8%B5_%D8%B9%D8%AF%D8%AF" title="ناقص عدد – ourdou" lang="ur" hreflang="ur" data-title="ناقص عدد" data-language-autonym="اردو" data-language-local-name="ourdou" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%8F%E6%95%B0" title="亏数 – chinois" lang="zh" hreflang="zh" data-title="亏数" data-language-autonym="中文" data-language-local-name="chinois" 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/Q467511#sitelinks-wikipedia" title="Modifier les liens interlangues" class="wbc-editpage">Modifier les liens</a></span></div> </div> </div> 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src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Aliquot_sum_40.svg/220px-Aliquot_sum_40.svg.png" decoding="async" width="220" height="297" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Aliquot_sum_40.svg/330px-Aliquot_sum_40.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Aliquot_sum_40.svg/440px-Aliquot_sum_40.svg.png 2x" data-file-width="460" data-file-height="621" /></a><figcaption>Diagramme en bâtons de la somme <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(n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d659eab6d8874e2cb6124fd2fc66b477b128c006" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.294ex; height:2.843ex;" alt="{\displaystyle s(n)}"></span> des diviseurs propres de <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> en fonction de <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>, pour <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> variant de 1 à 40. Les nombres déficients (gris) sont ceux pour lesquels le <i>bâton</i> reste sous la première diagonale. </figcaption></figure> <p>En <a href="/wiki/Math%C3%A9matiques" title="Mathématiques">mathématiques</a>, un <b>nombre déficient</b> est un nombre entier naturel <span class="texhtml mvar" style="font-style:italic;">n</span> qui est strictement supérieur à la somme de ses <a href="/wiki/Diviseur_strict" title="Diviseur strict">diviseurs stricts</a>, autrement dit, tel que <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 \sigma (n)<2n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo><</mo> <mn>2</mn> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma (n)<2n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3cdfee1e3828f02b97e5a1f58dea06cf169fe67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.189ex; height:2.843ex;" alt="{\displaystyle \sigma (n)<2n}"></span> où <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 \sigma (n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma (n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3213bbd075ed40d41d2b72dfaa4a190e031d3fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.534ex; height:2.843ex;" alt="{\displaystyle \sigma (n)}"></span> est la <a href="/wiki/Somme_des_diviseurs" class="mw-redirect" title="Somme des diviseurs">somme des diviseurs</a> entiers positifs de <span class="texhtml mvar" style="font-style:italic;">n</span> y compris <span class="texhtml mvar" style="font-style:italic;">n</span>. </p><p>La valeur <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 2n-\sigma (n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>n</mi> <mo>−</mo> <mi>σ</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2n-\sigma (n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2de6492fa9842b3d3711da4e2744eb4cd157eb98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.931ex; height:2.843ex;" alt="{\displaystyle 2n-\sigma (n)}"></span> est appelée <b>déficience</b> de <span class="texhtml mvar" style="font-style:italic;">n</span>. Les nombres dont la déficience est nulle sont les <a href="/wiki/Nombre_parfait" title="Nombre parfait">nombres parfaits</a>, et les nombres dont la déficience est strictement négative les <a href="/wiki/Nombre_abondant" title="Nombre abondant">nombres abondants</a>. </p><p>Les nombres déficients ont été introduits vers 130 <abbr class="abbr nowrap" title="après Jésus-Christ">apr. J.-C.</abbr> par <a href="/wiki/Nicomaque_de_G%C3%A9rase" title="Nicomaque de Gérase">Nicomaque de Gérase</a> dans son <i>Introduction à l'arithmétique</i>. </p><p>Leurs premières valeurs sont : 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, ... (voir suite <a href="//oeis.org/A005100" class="extiw" title="oeis:A005100">A005100</a> de l'<a href="/wiki/Encyclop%C3%A9die_en_ligne_des_suites_de_nombres_entiers" title="Encyclopédie en ligne des suites de nombres entiers">OEIS</a>). </p><p>Pour <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\geqslant 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>⩾</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geqslant 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fc9296c4967806b9a64fb5384a0b8f93d5ddf4c" 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\geqslant 2}"></span>, la déficience d'un nombre déficient va de 1 (pour les nombres dits <a href="/wiki/Nombre_presque_parfait" title="Nombre presque parfait">presque parfaits</a>) jusqu'à <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/fbd0b0f32b28f51962943ee9ede4fb34198a2521" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-1}"></span> pour les <a href="/wiki/Nombre_premier" title="Nombre premier">nombres premiers</a> (qui sont donc les naturels de déficience maximale). </p><p>Il existe une infinité de nombres déficients pairs et impairs. Par exemple, tous les <a href="/wiki/Nombre_premier" title="Nombre premier">nombres premiers</a> et leurs puissances (autrement dit, les <a href="/wiki/Nombre_primaire" title="Nombre primaire">nombres primaires</a>) sont déficients. Tout diviseur strict d'un parfait ou déficient est déficient. </p> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="2" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_Ensembles_de_divisibilit%C3%A9" title="Modèle:Palette Ensembles de divisibilité"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_Ensembles_de_divisibilit%C3%A9&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%"><a href="/wiki/Ensemble" title="Ensemble">Ensembles</a> d'<a href="/wiki/Entier_naturel" title="Entier naturel">entiers</a> sur la base de leur <a href="/wiki/Divisibilit%C3%A9" title="Divisibilité">divisibilité</a></div></th> </tr> <tr> <th class="navbox-group" style="">Formes de factorisation</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Nombre_premier" title="Nombre premier">Nombre premier</a></li> <li><a href="/wiki/Nombre_compos%C3%A9" title="Nombre composé">Nombre composé</a></li> <li><a href="/wiki/Nombre_puissant" title="Nombre puissant">Nombre puissant</a></li> <li><a href="/wiki/Entier_sans_facteur_carr%C3%A9" title="Entier sans facteur carré">Entier sans facteur carré</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Sommes de diviseurs</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Nombre_parfait" title="Nombre parfait">Nombre parfait</a></li> <li><a href="/wiki/Nombre_presque_parfait" title="Nombre presque parfait">Nombre presque parfait</a></li> <li><a href="/wiki/Nombre_quasi_parfait" title="Nombre quasi parfait">Nombre quasi parfait</a></li> <li><a href="/wiki/Nombre_parfait_multiple" title="Nombre parfait multiple">Nombre parfait multiple</a></li> <li><a href="/wiki/Nombre_h%C3%A9miparfait" title="Nombre hémiparfait">Nombre hémiparfait</a></li> <li><a href="/wiki/Nombre_hyperparfait" title="Nombre hyperparfait">Nombre hyperparfait</a></li> <li><a href="/wiki/Nombre_superparfait" title="Nombre superparfait">Nombre superparfait</a></li> <li><a href="/wiki/Nombre_unitairement_parfait" title="Nombre unitairement parfait">Nombre unitairement parfait</a></li> <li><a href="/wiki/Nombre_semi-parfait" title="Nombre semi-parfait">Nombre semi-parfait</a></li> <li><a href="/wiki/Nombre_semi-parfait_primitif" title="Nombre semi-parfait primitif">Nombre semi-parfait primitif</a></li> <li><a href="/wiki/Nombre_pratique" title="Nombre pratique">Nombre pratique</a></li> <li><a href="/wiki/Nombre_abondant" title="Nombre abondant">Nombre abondant</a></li> <li><a href="/wiki/Nombre_hautement_abondant" title="Nombre hautement abondant">Nombre hautement abondant</a></li> <li><a href="/wiki/Nombre_superabondant" title="Nombre superabondant">Nombre superabondant</a></li> <li><a href="/wiki/Nombre_colossalement_abondant" title="Nombre colossalement abondant">Nombre colossalement abondant</a></li> <li><a class="mw-selflink selflink">Nombre déficient</a></li> <li><a href="/wiki/Nombre_%C3%A9trange" title="Nombre étrange">Nombre étrange</a></li> <li><a href="/wiki/Nombre_intouchable" title="Nombre intouchable">Nombre intouchable</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Nombreux diviseurs</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Nombre_hautement_compos%C3%A9" title="Nombre hautement composé">Nombre hautement composé</a></li> <li><a href="/wiki/Nombre_hautement_compos%C3%A9_sup%C3%A9rieur" title="Nombre hautement composé supérieur">Nombre hautement composé supérieur</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Autre</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Nombres_amicaux" title="Nombres amicaux">Nombres amicaux</a></li> <li><a href="/wiki/Nombre_sociable" title="Nombre sociable">Nombre sociable</a></li> <li><a href="/wiki/Nombre_solitaire" title="Nombre solitaire">Nombre solitaire</a></li> <li><a href="/wiki/Nombre_sublime" title="Nombre sublime">Nombre sublime</a></li> <li><a href="/wiki/Nombre_%C3%A0_moyenne_harmonique_enti%C3%A8re" title="Nombre à moyenne harmonique entière">Nombre à moyenne harmonique entière</a></li> <li><a href="/wiki/Nombre_frugal" title="Nombre frugal">Nombre frugal</a></li> <li><a href="/wiki/Nombre_%C3%A9quidigital" title="Nombre équidigital">Nombre équidigital</a></li> <li><a href="/wiki/Nombre_extravagant" title="Nombre extravagant">Nombre extravagant</a></li></ul> </div></td> </tr> </tbody></table> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer skin-invert-image" typeof="mw:File"><a href="/wiki/Portail:Arithm%C3%A9tique_et_th%C3%A9orie_des_nombres" title="Arithmétique et théorie des nombres"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pascal%27s_triangle_5.svg/34px-Pascal%27s_triangle_5.svg.png" decoding="async" width="34" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pascal%27s_triangle_5.svg/50px-Pascal%27s_triangle_5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pascal%27s_triangle_5.svg/67px-Pascal%27s_triangle_5.svg.png 2x" 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