Bounds for odd k-perfect numbers

Authors

  • Chen Shi-Chao
  • Luo Hao

Keywords:

Odd perfect numbers, multiperfect numbers

Abstract

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 $(k-1)4^{r^3}$. doi:10.1017/S0004972711002462

Published

2011-10-27

Issue

Section

Articles