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A054991 revision #21

A054991
Number of prime divisors of n! - 1 (counted with multiplicity).
14
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.
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
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
editing