@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:-CVDPQB0Q-M
  skos:prefLabel "natural numbers"@en, "entier naturel"@fr ;
  a skos:Concept ;
  skos:narrower psr:-CSBDK0XG-N .

psr:-QBCKSDZ8-2
  skos:prefLabel "nombre parfait"@fr, "perfect number"@en ;
  a skos:Concept ;
  skos:related psr:-CSBDK0XG-N .

psr:-CSBDK0XG-N
  skos:related psr:-QBCKSDZ8-2 ;
  skos:definition """En théorie des nombres, un <b>nombre hémiparfait</b> est un entier naturel <i>n</i> dont la somme des diviseurs σ(<i>n</i>) est égale au produit de <i>n</i> et d'un demi-entier. Pour tout entier naturel <i>k</i> impair, on dit que <i>n</i> est <b><i>k</i>-hémiparfait</b> si <i>σ</i>(<i>n</i>) = <span class="texhtml"><span style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><i>k</i></span><span style="position:absolute;left:-10000px;top:auto;width:1px;height:1px;overflow:hidden">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">2</span></span></span> × <i>n</i>. Par exemple, 24 est 5-hémiparfait car <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 (24)=1+2+3+4+6+8+12+24=60={\\rac {5}{2}}\\	imes 24}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>σ<!-- σ --></mi>         <mo stretchy="false">(</mo>         <mn>24</mn>         <mo stretchy="false">)</mo>         <mo>=</mo>         <mn>1</mn>         <mo>+</mo>         <mn>2</mn>         <mo>+</mo>         <mn>3</mn>         <mo>+</mo>         <mn>4</mn>         <mo>+</mo>         <mn>6</mn>         <mo>+</mo>         <mn>8</mn>         <mo>+</mo>         <mn>12</mn>         <mo>+</mo>         <mn>24</mn>         <mo>=</mo>         <mn>60</mn>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>5</mn>             <mn>2</mn>           </mfrac>         </mrow>         <mo>×<!-- × --></mo>         <mn>24</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sigma (24)=1+2+3+4+6+8+12+24=60={\\rac {5}{2}}\\	imes 24}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f18a81017db0c4fcd6ebf025cf9f5f10a37d17d8" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:55.755ex; height:5.176ex;" alt="{\\\\displaystyle \\\\sigma (24)=1+2+3+4+6+8+12+24=60={\\rac {5}{2}}\\	imes 24}"></span>.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_h%C3%A9miparfait">https://fr.wikipedia.org/wiki/Nombre_h%C3%A9miparfait</a>)"""@fr, """In number theory, a <b>hemiperfect number</b> is a positive integer with a half-integer abundancy index. In other words, <i>σ</i>(<i>n</i>)/<i>n</i> = <i>k</i>/2 for an odd integer <i>k</i>, where <i>σ</i>(<i>n</i>) is the divisor function, the sum of all positive divisors of <i>n</i>. The first few hemiperfect numbers are:  <dl><dd>2, 24, 4320, 4680, 26208, 8910720, 17428320, 20427264, 91963648, 197064960, ... (sequence A159907 in the OEIS)</dd> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Hemiperfect_number">https://en.wikipedia.org/wiki/Hemiperfect_number</a>)"""@en ;
  a skos:Concept ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Nombre_h%C3%A9miparfait>, <https://en.wikipedia.org/wiki/Hemiperfect_number> ;
  skos:prefLabel "hemiperfect number"@en, "nombre hémiparfait"@fr ;
  skos:broader psr:-CVDPQB0Q-M, psr:-FM1M1PDT-5 ;
  dc:modified "2024-10-18"^^xsd:date ;
  dc:created "2023-07-26"^^xsd:date ;
  skos:inScheme psr: .

psr: a skos:ConceptScheme .
psr:-FM1M1PDT-5
  skos:prefLabel "suite d'entiers"@fr, "integer sequence"@en ;
  a skos:Concept ;
  skos:narrower psr:-CSBDK0XG-N .