bibkey: ordowski2020a306270 authors: Thomas Ordowski year: 2020 title: “OEIS A306270, composite k with b^(k(k-1)) = 1 mod k^2 for all b coprime to k, with the conjecture that its semiprimes > 4 are the p(p^2-p+1) of A190275” doi: null url: https://oeis.org/A306270 claim: “%N Composite numbers k such that b^(k(k-1)) == 1 (mod k^2) for every b coprime to k. %C Conjecture: all semiprimes > 4 in this sequence are in A190275. - Thomas Ordowski, Jul 19 2020” strata_touched:

• D5/S3/Arith/Congruence/OrdowskiSemiprimeCarmichaelSquareClassification license: citation-only triage: anchor

OEIS A306270

Thomas Ordowski’s 2020 comment conjectures the classification of every semiprime greater than four in A306270 by the semiprime family A190275.

Verified locator

• URL: https://oeis.org/A306270
• A306270 %N (verbatim): Composite numbers k such that b^(k(k-1)) == 1 (mod k^2) for every b coprime to k.
• A306270 %O (verbatim): 1,1
• A306270 %C (verbatim): These are composites k such that lambda(k^2) divides k(k-1), where lambda is the Carmichael function A002322.
• A306270 %C (verbatim): Conjecture: all semiprimes > 4 in this sequence are in A190275. - Thomas Ordowski, Jul 19 2020
• A306270 %C (verbatim): The conjecture was verified up to 1063290841. - Amiram Eldar, Jul 19 2020
• A190275 %N (verbatim): Semiprimes of the form p*(p^2 - p + 1).

Readings of 2026-09-16: the OEIS entry still marks the line Conjecture (2020-07-19) with only Eldar’s finite verification to 1063290841; OpenAlex "A306270" 0 hits; Math.SE API A306270 0 hits and b^(k(k-1)) mod k^2 semiprime 0 hits; GitHub code search in google-deepmind/formal-conjectures 0 hits. The Carmichael-function facts used are textbook; the named classification itself was not found in these surfaces. A GPT Pro reading of arxiv.org, openalex.org and math.stackexchange.com by A-number and by the defining phrases also found no proof; that reading is reported by the selection seat and is ASSUMED-UNVERIFIED. Historical openness beyond them is ASSUMED-UNVERIFIED.