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 σ(n)=kn. In this Paper, we show that for any integers r≥2,k≥2, the number of odd k-perfect numbers n with ω(n)≤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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