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Concept information

mathematical analysis > calculus > sequence > integer sequence > harmonic divisor number
number > natural numbers > harmonic divisor number

Preferred term

harmonic divisor number  

Definition

  • 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
    1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 (sequence A001599 in the OEIS).
    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.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Harmonic_divisor_number)

Broader concept

Synonym(s)

  • Ore number

In other languages

URI

http://data.loterre.fr/ark:/67375/PSR-MN1QTV32-L

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