A395791 Numbers k such that gcd(i!,k) = gcd((i-1)!,k) for some i <= A002034(k) not coprime to k.

10, 14, 18, 21, 22, 26, 28, 30, 33, 34, 38, 39, 42, 44, 46, 50, 51, 52, 54, 55, 56, 57, 58, 62, 65, 66, 68, 69, 70, 74, 75, 76, 78, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 114, 115, 116, 117, 118, 119, 122, 123, 124

Offset

1,1

Comments

If gcd(i!,k) > gcd((i-1)!,k), then clearly we have gcd(i,k) > 1 and that k does not divide (i-1)!. Sequence gives k such that the converse does not hold.

If k is squarefree, then k is a term if and only if (largest prime factor of k)/(smallest prime factor of k) > 2.

Links

Jianing Song, Table of n, a(n) for n = 1..10001

Example

10 is not a term since gcd(4!,10) = gcd(3!,10) = 2, and 4 is not coprime to 10.
1215 is not a term since gcd(10!,1215) = gcd(9!,1215) = 405, and 10 is not coprime to 1215.

Prog

(PARI) \\ See A395790.

Crossrefs

Cf. A002034. Complement of A395790.

Sequence in context: A096851 A244033 A121893 * A329390 A250197 A055985

Adjacent sequences: A395788 A395789 A395790 * A395792 A395793 A395794

Keyword

nonn

Author

Jianing Song, May 06 2026

Status

approved