bibkey: schulte2020a006472 authors: Werner Schulte year: 2020 title: “OEIS A006472, n!(n-1)!/2^(n-1), with the primality criterion n | 2 a(n-1) + 4 iff n is prime” doi: null url: https://oeis.org/A006472 claim: “%N a(n) = n!(n-1)!/2^(n-1). %C Conjecture: For n > 1, n divides 2a(n-1) + 4 if and only if n is prime. - Werner Schulte, Oct 04 2020” strata_touched:

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

OEIS A006472

Werner Schulte’s 2020 comment proposes a primality criterion for the sequence whose terms are the exact natural quotients n!*(n-1)!/2^(n-1). The formal result settles only the quoted Conjecture sentence, with its full range n > 1; no other comment or formula from the entry is claimed.

Verified locator

• URL: https://oeis.org/A006472

%N a(n) = n!*(n-1)!/2^(n-1).
%O 1,3
%C Conjecture: For n > 1, n divides 2*a(n-1) + 4 if and only if n is prime. - _Werner Schulte_, Oct 04 2020

Readings of 2026-09-16: the OEIS entry still marks the line Conjecture (added 2020-10-04) with no proof line; OpenAlex "A006472" 8 hits, none about this criterion; Math.SE API 0 hits; arXiv was not searched (no API response). Wilson’s theorem and the composite-factorial divisibility are textbook facts; the named criterion itself was not found in these surfaces. The repository’s closest frozen result is the A000680 sibling D5/S3/Arith/Congruence/SchulteHalfFactorialPrimeCriterion.result (a different criterion, (2n+1) ∣ (2n)!/2^n + 2^n ⟺ 2n+1 prime). Historical openness beyond them is ASSUMED-UNVERIFIED.