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arXiv · 2401.10427

Shifted-prime divisors

Steve Fan·Carl Pomerance
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Abstract

Let $\omega^*(n)$ 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 $\omega^*(n)$ are still somewhat a mystery. This paper addresses these higher moments and considers other related problems.

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Steve Fan, Carl Pomerance. 2024-01-18. Shifted-prime divisors. https://arxiv.org/abs/2401.10427

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