bibkey: rotondo2020a006972 authors: Davide Rotondo year: 2020 title: “OEIS A006972, Lucas-Carmichael numbers, with Rotondo’s sufficient condition for three distinct odd prime factors” doi: null url: https://oeis.org/A006972 claim: “%N Lucas-Carmichael numbers: squarefree composite numbers k such that p | k => p+1 | k+1. %C Conjecture: if k = pqr, p = ad - 1, q = bd - 1, r = cd - 1 are distinct odd primes, with d = gcd(p + 1, q + 1, r + 1) and abcd divides k + 1, then k is a Lucas-Carmichael number. - Davide Rotondo, Dec 23 2020” strata_touched:
- D5/S3/Arith/Congruence/RotondoLucasCarmichaelCriterion license: citation-only triage: anchor
OEIS A006972
Davide Rotondo’s 2020 comment gives a sufficient condition for a product of three distinct odd primes to be a Lucas-Carmichael number.
Verified locator
- URL: https://oeis.org/A006972
- A006972
%N(verbatim): Lucas-Carmichael numbers: squarefree composite numbers k such that p | k => p+1 | k+1. - A006972
%C(verbatim): Conjecture: if k = pqr, p = ad - 1, q = bd - 1, r = cd - 1 are distinct odd primes, with d = gcd(p + 1, q + 1, r + 1) and abcd divides k + 1, then k is a Lucas-Carmichael number. - Davide Rotondo, Dec 23 2020
Reading dated 2026-09-17: the entry still labels this sentence Conjecture,
contains no %F line, and carries no settlement marker. Full-text readings of
every paper linked by %H, together with the corresponding Wikipedia and
MathWorld pages, found no proof or refutation of this criterion. Historical
openness outside those sources is ASSUMED-UNVERIFIED.