On the number of factorizations of an integer

2016/09/27 by Balasubramanian, R., Srivastav, Priyamvad · 1 citation
#05A99 #FOS: Mathematics #Number Theory (math.NT) #Primary: 11A51 #Secondary: 11B73

paper · doi:10.48550/arxiv.1609.08602

Abstract

Let f(n) denote the number of unordered factorizations of a positive integer n into factors larger than 1. We show that the number of distinct values of f(n), less than or equal to x, is at most exp ( C √((log x)/(log log x)) ( 1 + o(1) ) ), where C=2π√(2/3) and x is sufficiently large. This improves upon a previous result of the first author and F. Luca.

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