Numbers whose positive divisors have small integral harmonic mean

Author:
G. L. Cohen

Journal:
Math. Comp. **66** (1997), 883-891

MSC (1991):
Primary 11A25, 11Y70

DOI:
https://doi.org/10.1090/S0025-5718-97-00819-3

MathSciNet review:
1397443

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Abstract: A natural number is said to be harmonic when the harmonic mean of its positive divisors is an integer. These were first introduced almost fifty years ago. In this paper, all harmonic numbers less than are listed, along with some other useful tables, and all harmonic numbers with are determined.

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Additional Information

**G. L. Cohen**

Affiliation:
School of Mathematical Sciences, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia

Email:
glc@maths.uts.edu.au

DOI:
https://doi.org/10.1090/S0025-5718-97-00819-3

Received by editor(s):
July 7, 1994

Received by editor(s) in revised form:
March 29, 1996

Dedicated:
To Peter Hagis, Jr., on the occasion of his 70th birthday

Article copyright:
© Copyright 1997
American Mathematical Society