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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Unitary harmonic numbers
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by Peter Hagis and Graham Lord PDF
Proc. Amer. Math. Soc. 51 (1975), 1-7 Request permission

Abstract:

If ${d^ \ast }(n)$ and ${\sigma ^ \ast }(n)$ denote the number and sum, respectively, of the unitary divisors of the natural number $n$ then the harmonic mean of the unitary divisors of $n$ is given by ${H^ \ast }(n) = n{d^ \ast }(n)/{\sigma ^ \ast }(n)$. Here we investigate the properties of ${H^ \ast }(n)$, and, in particular, study those numbers $n$ for which ${H^ \ast }(n)$ is an integer.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 1-7
  • MSC: Primary 10A20
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0369231-9
  • MathSciNet review: 0369231