Article contents
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
- Type
- Research Article
- Information
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
References
- 2
- Cited by