An upper bound for the number of odd multiperfect numbers

Authors

  • P. Yuan South China Normal University

Keywords:

Odd perfect numbers, \(k\)-perfect numbers

Abstract

A natural number \(n\) is called \(k\)-perfect if \(\sigma(n) = kn\). In this Paper, we show that for any integers \(r\ge2, k\ge2\), the number of odd \(k\)-perfect numbers \(n\) with \(\omega(n)\le r\) is bounded by \({\lfloor4^r\log_3 2\rfloor+r\choose r} \sum_{i=1}^r {kr/2\choose i} \), which is less than \(4^{r^2}\) when \(r\) is enough large. 10.1017/S000497271200113X

Published

2013-12-02

Issue

Vol. 89 No. 1 (2014)

Section

Articles
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