Quasiperfect numbers with the same exponent

2016/10/04 by Yamada, Tomohiro
#11A25 #11A36 #11Y05 #11Y70 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1610.01063

Abstract

We study some divisibility properties of quasiperfect numbers. We show that if N=(p₁ p₂ ⋯ p_t)^2a=m² is quasiperfect, then 2a+1 is divisible by 3 and N has at least one prime factor smaller than exp 716.7944. Moreover, we find some lower bounds concerning quasiperfect numbers of the form N=m² with m squarefree.

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