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

Tomohiro Yamada

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

Tomohiro Yamada

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Abstract

We study some divisibility properties of multiperfect numbers. Our main result is: if $N=p_1^{α_1}... p_s^{α_s} q_1^{2β_1}... q_t^{2β_t}$ with $β_1, ..., β_t$ in some finite set S satisfies $σ(N)=\frac{n}{d}N$, then N has a prime factor smaller than C, where C is an effective computable constant depending only on s, n, S.

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Tomohiro Yamada. 2007-07-31. On the divisibility of odd perfect numbers by a high power of a prime. https://arxiv.org/abs/math/0511410

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