The On-Line Encyclopedia of Integer Sequences (OEIS)

A054991 revision #12

A054991

Number of prime divisors of n! - 1.

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

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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

Table of n, a(n) for n=1..78.

R. G. Wilson v, Explicit factorizations

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}] (* From Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

CROSSREFS

Cf. A054988, A054989, A054990, A054992.

Sequence in context: A087917 A330334 A087741 * * A302918 A316149

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 (rgwv(AT)rgwv.com), Mar 24 2001

STATUS

approved