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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 (list; graph; refs; listen; history; text; internal format)
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
R. G. Wilson v, Explicit factorizations
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
Sequence in context: A087917 A330334 A087741 * A302918 A316149 A047071
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

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)