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The constant factor in the asymptotic for practical numbers

2019/06/18 by Weingartner, Andreas
#11N25 #11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1906.07819

Abstract

An integer n≥ 1 is said to be practical if every natural number m ≤ n can be expressed as a sum of distinct positive divisors of n. The number of practical numbers up to x is asymptotic to c x/log x, where c is a constant. In this note we show that c=1.33607....

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