bibkey: krizek2014a249759 authors: Jaroslav Krizek year: 2014 title: “OEIS A249759, primes p for which sigma(p-1) is prime” doi: null url: https://oeis.org/A249759 claim: “Primes p such that sigma(p-1) is a prime q. Conjectures: 1) sequence is finite; 2) sequence is a subsequence of A019434 (Fermat primes); 3) sequence consists of Fermat primes p such that sigma(p-1) is a Mersenne prime; 4) a(n) = (A249761(n)+3)/2.” strata_touched:

• D5/S3/Arith/Mersenne/KrizekSigmaPrimeFermatMersenne license: citation-only triage: anchor

OEIS A249759

Krizek’s entry lists primes p for which the divisor sum of p - 1 is prime. The formal result settles only items 2 and 3 of the quoted conjecture: every such p has Fermat-prime form, and its divisor sum has Mersenne-prime form. Item 1, finiteness of this class of Fermat primes, remains open. Item 4 concerns the definition of the separate sequence A249761 and is not claimed.

Verified locator

• URL: https://oeis.org/A249759
• Revision: #40, Sep 10 2025 16:53:46
• A249759 %N (verbatim): Primes p such that sigma(p-1) is a prime q.
• A249759 %S (verbatim): 3,5,17,65537
• A249759 %C (verbatim): Conjectures: 1) sequence is finite; 2) sequence is a subsequence of A019434 (Fermat primes); 3) sequence consists of Fermat primes p such that sigma(p-1) is a Mersenne prime; 4) a(n) = (A249761(n)+3)/2.
• A249759 %A (verbatim): Jaroslav Krizek, Nov 13 2014

The 2026-09-15 literature check found the conjecture unchanged in the current OEIS entry, with no %D bibliography and no %H literature link. The entry still marks all four items as conjectures. Google Scholar and MathSciNet were not checked; exhaustive historical priority is ASSUMED-UNVERIFIED.