A395286 Positive integers m such that gcd(m^10 - 1, m! - 1) > 1.

9, 15, 29, 52

Offset

1,1

Comments

For m = 9, gcd(m^10 - 1, m! - 1) = 121 = 11^2, and this shows that there exist integers m > 1 and k > 1 such that gcd(m^k - 1, m! - 1) is not squarefree.

No additional terms are known for m <= 100000 (it is not known whether the sequence is finite).

No additional terms for m <= 5*10^6. - Michael S. Branicky, May 01 2026

Links

Table of n, a(n) for n=1..4.

Example

15 and 29 are terms since gcd(15^10 - 1, 15! - 1) = gcd(29^10 - 1, 29! - 1) = 31.

Prog

(PARI) isok(m) = gcd(m^10 - 1, m! - 1) > 1; \\ Michel Marcus, Apr 20 2026
(Python)
import math
def isok(m): return math.gcd(m**10-1, math.factorial(m)-1) > 1  # Jwalin Bhatt, Apr 28 2026

Crossrefs

Cf. A033312, A069095.

Sequence in context: A046356 A248381 A060874 * A147511 A124580 A103508

Adjacent sequences: A395283 A395284 A395285 * A395287 A395288 A395289

Keyword

nonn,hard,more

Author

Marco Ripà, Apr 18 2026

Status

approved