A351709 a(n) = Sum_{p|n, p prime} p!.

0, 2, 6, 2, 120, 8, 5040, 2, 6, 122, 39916800, 8, 6227020800, 5042, 126, 2, 355687428096000, 8, 121645100408832000, 122, 5046, 39916802, 25852016738884976640000, 8, 120, 6227020802, 6, 5042, 8841761993739701954543616000000, 128, 8222838654177922817725562880000000

Offset

1,2

Comments

Inverse Möbius transform of n! * c(n), where c(n) is the characteristic function of primes (A010051). - Wesley Ivan Hurt, Apr 01 2025

Links

Table of n, a(n) for n=1..31.

Formula

a(n) = Sum_{d|n} d! * c(d), where c = A010051. - Wesley Ivan Hurt, Apr 01 2025

Example

a(6) = 8; a(6) = Sum_{p|6} p! = 2! + 3! = 2*1 + 3*2*1 = 8.

Crossrefs

Cf. A000040, A000142, A010051, A062363, A351708.

Sequence in context: A086660 A271503 A102068 * A188733 A104290 A152549

Adjacent sequences: A351706 A351707 A351708 * A351710 A351711 A351712

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 16 2022

Status

approved