2024/01/18 by Steve Fan, Carl Pomerance, Fan, Steve +1 · 1 citation
Mathematics · #11B05 #11N25 #11N37 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2401.10427
openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let ω^*(n) denote the number of divisors of n that are shifted primes, that is, the number of divisors of n of the form p-1, with p prime. Studied by Prachar in an influential paper from 70 years ago, the higher moments of ω^*(n) are still somewhat a mystery. This paper addresses these higher moments and considers other related problems.