On a Problem by Erdős and Mirsky on the ratio of the number of divisors of consecutive integers

2025/03/31 by Jan-Christoph Schlage-Puchta, Schlage-Puchta, Jan-Christoph
Mathematics · #11A25 #11N36 #Analytic Number Theory Research #Benford’s Law and Fraud Detection #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.11463

openalex publication_date 2025/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L be the closure of the set of all real numbers α, such that there exist infinitely many integers n, such that α=log(d(n+1))/(d(n)), where d is the number of divisors of n. We give improved lower bounds for the density of L.

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