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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the largest prime divisor of an odd harmonic number
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by Yusuke Chishiki, Takeshi Goto and Yasuo Ohno PDF
Math. Comp. 76 (2007), 1577-1587 Request permission


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 $10^5$.
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Additional Information
  • Yusuke Chishiki
  • Affiliation: Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan
  • Takeshi Goto
  • Affiliation: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan
  • Email:
  • Yasuo Ohno
  • Affiliation: Department of Mathematics, Kinki University Higashi-Osaka, Osaka 577-8502, Japan
  • Email:
  • Received by editor(s): September 29, 2005
  • Received by editor(s) in revised form: February 15, 2006
  • Published electronically: January 30, 2007
  • Additional Notes: The third author was supported in part by JSPS Grant-in-Aid No. 15740025.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 1577-1587
  • MSC (2000): Primary 11A25, 11Y70
  • DOI:
  • MathSciNet review: 2299789