id:A054991 - OEIS Search Results

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Number of prime divisors of n! - 1.

+0
6

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; listen)

	OFFSET	`1,5`
	COMMENT	`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` `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}]]`
	CROSSREFS	`Cf. A054988, A054989, A054990, A054992.` `Sequence in context: A114919 A087917 A087741 this_sequence A047071 A124287 A060240` `Adjacent sequences: A054988 A054989 A054990 this_sequence A054992 A054993 A054994`
	KEYWORD	`nonn`
	AUTHOR	`Arne Ring (arne.ring(AT)epost.de), May 30 2000`
	EXTENSIONS	`More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 24 2001`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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