Bounds for Odd $k$-Perfect Numbers

Details Bounds for Odd $k$-Perfect Numbers Bounds for Odd $k$-Perfect Numbers

2011-02-22

arxiv.org/abs/1102.4397v1

Mathematics

Number Theory

6 pages

Scientific paper

Let $k\ge2$ be an integer. A natural number $n$ is called $k$-perfect if
$\sigma(n)=kn.$ For any integer $r\ge1$ we prove that the number of odd
$k$-perfect numbers with at most $r$ distinct prime factors is bounded by
$k4^{r^3}$.

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