An upper bound for the number of odd multiperfect numbers

P. Yuan

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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