@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-RTZKCZJZ-P
  skos:broader psr:-CVDPQB0Q-M, psr:-FM1M1PDT-5 ;
  skos:related psr:-QBCKSDZ8-2, psr:-T9B5VHTP-V ;
  skos:prefLabel "nombre sociable"@fr, "sociable number"@en ;
  skos:definition """En mathématiques, un nombre entier strictement positif est <b>sociable d'ordre <i>n</i></b> si sa suite aliquote est fermée et compte <i>n</i> maillons. La formule de construction d'une suite aliquote est la suivante : <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 a_{i+1}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>i</mi>             <mo>+</mo>             <mn>1</mn>           </mrow>         </msub>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{i+1}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/714e1a37379d8e664890d0385b0bd842df2ad6e5" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.13ex; height:2.009ex;" alt="{\\\\displaystyle a_{i+1}}"></span> est la somme des diviseurs stricts 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 a_{i}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>i</mi>           </mrow>         </msub>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{i}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="a_{i}"></span> (les diviseurs 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 a_{i}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>i</mi>           </mrow>         </msub>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{i}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="a_{i}"></span> strictement compris entre 0 et <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 a_{i}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>i</mi>           </mrow>         </msub>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{i}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="a_{i}"></span>). Les nombres amicaux sont sociables d'ordre 2, les parfaits sociables d'ordre 1. Le premier autre nombre sociable (d'ordre 5) fut découvert par Paul Poulet, un mathématicien belge, en 1918 : 12 496 → 14 288 → 15 472 → 14 536 → 14 264 (→ 12 496). En 1970, le Français Henri Cohen en découvre sept d'ordre 4. On n'en connaît aucun d'ordre 3 ni 7. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_sociable">https://fr.wikipedia.org/wiki/Nombre_sociable</a>)"""@fr, """In mathematics, sociable numbers are numbers whose aliquot sums form a periodic sequence. They are generalizations of the concepts of perfect numbers and amicable numbers. The first two sociable sequences, or sociable chains, were discovered and named by the Belgian mathematician Paul Poulet in 1918. In a sociable sequence, each number is the sum of the proper divisors of the preceding number, i.e., the sum excludes the preceding number itself. For the sequence to be sociable, the sequence must be cyclic and return to its starting point. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Sociable_number">https://en.wikipedia.org/wiki/Sociable_number</a>)"""@en ;
  a skos:Concept ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Sociable_number>, <https://fr.wikipedia.org/wiki/Nombre_sociable> ;
  dc:created "2023-07-26"^^xsd:date ;
  skos:inScheme psr: ;
  dc:modified "2024-10-18"^^xsd:date .

psr:-CVDPQB0Q-M
  skos:prefLabel "natural numbers"@en, "entier naturel"@fr ;
  a skos:Concept ;
  skos:narrower psr:-RTZKCZJZ-P .

psr:-QBCKSDZ8-2
  skos:prefLabel "nombre parfait"@fr, "perfect number"@en ;
  a skos:Concept ;
  skos:related psr:-RTZKCZJZ-P .

psr:-T9B5VHTP-V
  skos:prefLabel "amicable numbers"@en, "nombres amicaux"@fr ;
  a skos:Concept ;
  skos:related psr:-RTZKCZJZ-P .

psr: a skos:ConceptScheme .
psr:-FM1M1PDT-5
  skos:prefLabel "suite d'entiers"@fr, "integer sequence"@en ;
  a skos:Concept ;
  skos:narrower psr:-RTZKCZJZ-P .