@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: a skos:ConceptScheme .
psr:-CVDPQB0Q-M
  skos:prefLabel "natural numbers"@en, "entier naturel"@fr ;
  a skos:Concept ;
  skos:narrower psr:-MN1QTV32-L .

psr:-FM1M1PDT-5
  skos:prefLabel "suite d'entiers"@fr, "integer sequence"@en ;
  a skos:Concept ;
  skos:narrower psr:-MN1QTV32-L .

psr:-MN1QTV32-L
  dc:modified "2024-10-18"^^xsd:date ;
  dc:created "2023-07-26"^^xsd:date ;
  skos:broader psr:-FM1M1PDT-5, psr:-CVDPQB0Q-M ;
  skos:definition """En arithmétique, un <b>nombre à moyenne harmonique entière</b> est un entier strictement positif dont les diviseurs positifs ont pour moyenne harmonique un nombre entier. Autrement dit, si <i>a</i><sub>1</sub>, <i>a</i><sub>2</sub>, ..., <i>a</i><sub><i>n</i></sub> sont les diviseurs du nombre,   <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 {\\rac {n}{{\\rac {1}{a_{1}}}+{\\rac {1}{a_{2}}}+\\\\cdots +{\\rac {1}{a_{n}}}}}={\\rac {n}{\\\\sum _{i=1}^{n}{\\rac {1}{a_{i}}}}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mi>n</mi>             <mrow>               <mrow class="MJX-TeXAtom-ORD">                 <mfrac>                   <mn>1</mn>                   <msub>                     <mi>a</mi>                     <mrow class="MJX-TeXAtom-ORD">                       <mn>1</mn>                     </mrow>                   </msub>                 </mfrac>               </mrow>               <mo>+</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mfrac>                   <mn>1</mn>                   <msub>                     <mi>a</mi>                     <mrow class="MJX-TeXAtom-ORD">                       <mn>2</mn>                     </mrow>                   </msub>                 </mfrac>               </mrow>               <mo>+</mo>               <mo>⋯<!-- ⋯ --></mo>               <mo>+</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mfrac>                   <mn>1</mn>                   <msub>                     <mi>a</mi>                     <mrow class="MJX-TeXAtom-ORD">                       <mi>n</mi>                     </mrow>                   </msub>                 </mfrac>               </mrow>             </mrow>           </mfrac>         </mrow>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mi>n</mi>             <mrow>               <munderover>                 <mo>∑<!-- ∑ --></mo>                 <mrow class="MJX-TeXAtom-ORD">                   <mi>i</mi>                   <mo>=</mo>                   <mn>1</mn>                 </mrow>                 <mrow class="MJX-TeXAtom-ORD">                   <mi>n</mi>                 </mrow>               </munderover>               <mrow class="MJX-TeXAtom-ORD">                 <mfrac>                   <mn>1</mn>                   <msub>                     <mi>a</mi>                     <mrow class="MJX-TeXAtom-ORD">                       <mi>i</mi>                     </mrow>                   </msub>                 </mfrac>               </mrow>             </mrow>           </mfrac>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {n}{{\\rac {1}{a_{1}}}+{\\rac {1}{a_{2}}}+\\\\cdots +{\\rac {1}{a_{n}}}}}={\\rac {n}{\\\\sum _{i=1}^{n}{\\rac {1}{a_{i}}}}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89ab1a11391e12f04695e8e8475291ea26402196" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:31.832ex; height:6.343ex;" alt="{\\rac  n{{\\rac  1{a_{1}}}+{\\rac  1{a_{2}}}+\\\\cdots +{\\rac  1{a_{n}}}}}={\\rac  n{\\\\sum _{{i=1}}^{n}{\\rac  1{a_{i}}}}}"></span></dd></dl> doit être un entier. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_%C3%A0_moyenne_harmonique_enti%C3%A8re">https://fr.wikipedia.org/wiki/Nombre_%C3%A0_moyenne_harmonique_enti%C3%A8re</a>)"""@fr, """In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are
<br/>     1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 (sequence A001599 in the OEIS).
<br/>Harmonic divisor numbers were introduced by Øystein Ore, who showed that every perfect number is a harmonic divisor number and conjectured that there are no odd harmonic divisor numbers other than 1.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Harmonic_divisor_number">https://en.wikipedia.org/wiki/Harmonic_divisor_number</a>)"""@en ;
  a skos:Concept ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Harmonic_divisor_number>, <https://fr.wikipedia.org/wiki/Nombre_%C3%A0_moyenne_harmonique_enti%C3%A8re> ;
  skos:prefLabel "harmonic divisor number"@en, "nombre à moyenne harmonique entière"@fr ;
  skos:altLabel "Ore number"@en ;
  skos:inScheme psr: .