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A054991
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Number of prime divisors of n! - 1.
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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| The series is related to the product of primes and the "proof" of the existence of infinite many prime twins.
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LINKS
| R. G. Wilson v, Explicit factorizations
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
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EXAMPLE
| a(2)=0 because 2! - 1 = 1 (and this is not a prime number) a(5)=2 because 5! -1 = 119 = 7 * 17
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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}] (* From Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
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CROSSREFS
| Cf. A054988, A054989, A054990, A054992.
Sequence in context: A114919 A087917 A087741 * A047071 A124287 A060240
Adjacent sequences: A054988 A054989 A054990 * A054992 A054993 A054994
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KEYWORD
| nonn
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AUTHOR
| Arne Ring (arne.ring(AT)epost.de), May 30 2000
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 24 2001
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