Upper bounds on the second largest prime factor of an odd perfect number

2018/10/28 by Zelinsky, Joshua · 1 citation
#11A05 (Primary) #11A25 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.11734

Abstract

Acquaah and Konyagin showed that if N is an odd perfect number where N= p₁^a₁p₂^a₂ ⋯ p_k^a_k where p₁ < p₂ ⋯ < p_k then one must have p_k < 3^1/3N^1/3. Using methods similar to theirs, we show that p_k-1< (2N)^1/5 and that p_k-1p_k < 6^1/4N^1/2. We also show that if p_k and p_k-1 are close to each other than these bounds can be further strengthened.

Cited by

• On near superperfect numbers, the Goormaghtigh conjecture, and Mertens' theorem

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