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IMPROVED UPPER BOUNDS FOR ODD MULTIPERFECT NUMBERS
Published online by Cambridge University Press: 12 June 2013
Abstract
In this paper, we prove that, if $N$ is a positive odd number with
$r$ distinct prime factors such that
$N\mid \sigma (N)$, then
$N\lt {2}^{{4}^{r} - {2}^{r} } $ and
$N{\mathop{\prod }\nolimits}_{p\mid N} p\lt {2}^{{4}^{r} } $, where
$\sigma (N)$ is the sum of all positive divisors of
$N$. In particular, these bounds hold if
$N$ is an odd perfect number.
MSC classification
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- Research Article
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- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
References
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