A054991 Number of prime divisors of n! - 1 (counted with multiplicity).

0, 0, 1, 1, 2, 1, 1, 2, 3, 2, 4, 1, 2, 1, 5, 2, 3, 3, 3, 2, 4, 3, 2, 2, 3, 2, 2, 4, 5, 1, 3, 1, 1, 2, 3, 2, 5, 1, 4, 2, 4, 4, 7, 4, 5, 5, 2, 4, 3, 2, 5, 5, 4, 6, 6, 5, 6, 5, 2, 3, 4, 4, 5, 4, 6, 4, 7, 2, 6, 5, 5, 3, 4, 5, 7, 3, 5, 4, 2, 4, 4, 4, 4, 6, 2, 3, 4

Offset

1,5

Comments

The series is related to the product of primes and the "proof" of the existence of infinite many prime twins.

Links

Amiram Eldar, Table of n, a(n) for n = 1..135

R. G. Wilson v, Explicit factorizations

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Example

a(2)=0 because 2! - 1 = 1 (and this is not a prime number) a(5)=2 because 5! -1 = 119 = 7 * 17

Mathematica

a[q_] := Module[{x, n}, x=FactorInteger[q!-1]; n=Length[x]; Sum[Table[x[[i]][[2]], {i, n}][[j]], {j, n}]]
A054991[n_Integer] := PrimeOmega[n! - 1]; A054991[1] = 0; Table[A054991[n], {n, 2, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

Crossrefs

Cf. A033312, A054988, A054989, A054990, A054992.

Sequence in context: A087917 A330334 A087741 * A302918 A316149 A047071

Adjacent sequences: A054988 A054989 A054990 * A054992 A054993 A054994

Keyword

nonn

Author

Arne Ring (arne.ring(AT)epost.de), May 30 2000

Extensions

More terms from Robert G. Wilson v, Mar 24 2001

More terms from Amiram Eldar, Oct 03 2019

Status

approved