On factorizations into coprime parts

2021/02/01 by Just, Matthew, Lebowitz-Lockard, Noah
#11A25 #11A51 #11N56 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.00978

Abstract

Let f(n) and g(n) be the number of unordered and ordered factorizations of n into integers larger than one. Let F(n) and G(n) have the additional restriction that the factors are coprime. We establish the asymptotic bounds for the sums of F(n)^β and G(n)^β up to x for all real β and the asymptotic bounds for f(n)^β and g(n)^β for all negative β.

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