## 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
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## 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 $1$.

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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