On the divisibility of odd perfect numbers by a high power of a prime

Abstract

We study some divisibility properties of multiperfect numbers. Our main result is: if $N=p_1^{{\alpha }_1}...p_s^{{\alpha }_s}{q}_1^{2{\beta }_1}...q_t^{2{\beta }_t}$ with ${\beta }_1,...,{\beta }_t$ in some finite set S satisfies $\sigma (N)=\frac{n}{d}N$, then N has a prime factor smaller than C, where C is an effective computable constant depending only on s, n, S.

arXiv comment13 pages

References in corpus (1)

• A Proof of the Odd Perfect Number Conjecture

Cited by in corpus (1)

• Bounds On Factors Of Odd Perfect Numbers