On the largest prime divisor of an odd harmonic number

Yusuke Chishiki, Takeshi Goto, Yasuo Ohno

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

A positive integer is called a (Ore's) harmonic number if its positive divisors have integral harmonic mean. Ore conjectured that every harmonic number greater than 1 is even. If Ore's conjecture is true, there exist no odd perfect numbers. In this paper, we prove that every odd harmonic number greater than 1 must be divisible by a prime greater than 105.

Original languageEnglish
Pages (from-to)1577-1587
Number of pages11
JournalMathematics of Computation
Volume76
Issue number259
DOIs
Publication statusPublished - 2007 Jul
Externally publishedYes

Keywords

  • Cyclotomic numbers
  • Harmonic numbers
  • Perfect numbers

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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