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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 2024 MCQ for Mathematics of Computation is 1.78.

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All numbers whose positive divisors have integral harmonic mean up to $\mathbf {300}$
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by T. Goto and S. Shibata;
Math. Comp. 73 (2004), 475-491
DOI: https://doi.org/10.1090/S0025-5718-03-01554-0
Published electronically: June 19, 2003

Abstract:

A positive integer $n$ is said to be harmonic when the harmonic mean $H(n)$ of its positive divisors is an integer. Ore proved that every perfect number is harmonic. No nontrivial odd harmonic numbers are known. In this article, the list of all harmonic numbers $n$ with $H(n) \le 300$ is given. In particular, such harmonic numbers are all even except $1$.
References
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Bibliographic Information
  • T. Goto
  • Affiliation: Graduate School of Mathematics, Kyushu University 33, Fukuoka 812-8581, Japan
  • Address at time of publication: Department of Mathematics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
  • Email: tgoto@math.kyushu-u.ac.jp, goto_takeshi@ma.noda.tus.ac.jp
  • S. Shibata
  • Affiliation: Faculty of Mathematics, Kyushu University 33, Fukuoka 812-8581, Japan
  • Email: ma200019@math.kyushu-u.ac.jp
  • Received by editor(s): December 10, 2001
  • Received by editor(s) in revised form: July 17, 2002
  • Published electronically: June 19, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 73 (2004), 475-491
  • MSC (2000): Primary 11A25, 11Y70
  • DOI: https://doi.org/10.1090/S0025-5718-03-01554-0
  • MathSciNet review: 2034133