On the divisibility of odd perfect numbers, quasiperfect numbers and amicable numbers by a high power of a prime

Tomohiro Yamada

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arXiv · 1609.08795

On the divisibility of odd perfect numbers, quasiperfect numbers and amicable numbers by a high power of a prime

Tomohiro Yamada

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Abstract

We shall give an explicit upper bound for the smallest prime factor of multiperfect numbers of the form $N=p_1^{\alpha_1}\cdots p_s^{\alpha_s} q_1^{\beta_1}\cdots q_t^{\beta_t}$ with $\beta_1, \ldots, \beta_t$ bounded by a given constant. We shall also give similar results for quasiperfect numbers and relatively prime amicable pairs of opposite parity.

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Tomohiro Yamada. 2016-09-28. On the divisibility of odd perfect numbers, quasiperfect numbers and amicable numbers by a high power of a prime. https://arxiv.org/abs/1609.08795

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