Pith. sign in

REVIEW 2 cited by

Shifted-prime divisors

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2401.10427 v5 pith:WBQ7ROON submitted 2024-01-18 math.NT

Steve Fan , Carl Pomerance This is my paper · ORCID
classification math.NT
keywords divisorshighermomentsnumberomegaaddressesconsidersdenote
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Moments of the shifted prime divisor function

    math.NT 2025-05 accept novelty 8.0 of 10

    For every k≥2, the k-th moment of the shifted-prime divisor function is asymptotically of order x(log x)^(2^k-k-1), confirming the Fan-Pomerance conjecture.

  2. Short intervals for the Romanoff-type sumset

    math.NT 2026-02 unverdicted novelty 6.0 of 10

    Most short intervals of length X^theta (theta > 2/15 + eps) contain asymptotically h integers of the form p + a with p prime and a in the lacunary set A_lambda(X).

Pith tools