An Erdős-Kac theorem for integers with dense divisors

2022/11/10 by Tenenbaum, Gérald, Weingartner, Andreas
#11N25 #11N37 #11N60 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2211.05819

Abstract

We show that for large integers n, whose ratios of consecutive divisors are bounded above by an arbitrary constant, the number of prime factors follows an approximate normal distribution, with mean C log₂ n and variance V log₂ n, where C=1/(1-e^-γ)≈ 2.280 and V≈ 0.414. This result is then generalized in two different directions.

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