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 A054991 Number of prime divisors of n! - 1 (counted with multiplicity). 9
 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 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. 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

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Last modified February 20 20:08 EST 2020. Contains 332084 sequences. (Running on oeis4.)