2014/05/11 by Andreas Weingartner, Weingartner, Andreas
Mathematics · #11N25 #11N37 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11N25 #msc:11N37
paper · pdf · doi:10.48550/arxiv.1405.2585
Minor improvement of Theorems 2 and 4. To appear in Q. J. Math
arxiv created 2015/03/03 · arxiv updated 2015/03/04
An integer n is called practical if every m≤ n can be written as a sum of distinct divisors of n. We show that the number of practical numbers below x is asymptotic to c x/log x, as conjectured by Margenstern. We also give an asymptotic estimate for the number of integers below x whose maximum ratio of consecutive divisors is at most t, valid uniformly for t≥ 2.