Improved upper bounds for odd multiperfect numbers

Y.-G. Chen; C.-E. Tang

Improved upper bounds for odd multiperfect numbers

Authors

Y.-G. Chen Nanjing Normal University
C.-E. Tang Nanjing Normal University

Keywords:

odd perfect numbers, multiple perfect numbers, upper bound

Abstract

Suppose

$N$ be a positive odd number with

$r$ distinct prime factors and

$N$ divides

$\sigma(N)$ where

$\sigma(N)$ is the sum of the positive divisors of

$N$ . In this paper, we prove upper bounds for

$N$ and the radical of

$N$ in terms of

$r$ . In particular, these bounds hold if

$N$ is an odd perfect number. DOI: 10.1017/S0004972713000488

Author Biography

Y.-G. Chen, Nanjing Normal University

School of Mathematical Sciences, Professor

Published

2014-03-25

Issue

Vol. 89 No. 3 (2014)

Section

Articles

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