A054990 Number of prime divisors of n! + 1 (counted with multiplicity).

1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 1, 3, 2, 2, 3, 5, 3, 6, 2, 2, 3, 3, 4, 2, 2, 2, 1, 2, 3, 5, 4, 4, 5, 2, 5, 6, 1, 2, 4, 7, 1, 3, 4, 3, 3, 3, 4, 2, 5, 5, 6, 4, 4, 2, 2, 4, 3, 4, 2, 4, 4, 3, 5, 3, 4, 5, 4, 5, 6, 5, 2, 7, 1, 4, 2, 3, 1, 6, 3, 4, 7, 3, 3, 3, 5, 5, 4, 3, 8, 3, 6, 2, 4, 3, 4, 5, 6, 6, 5, 5, 4, 5

Offset

1,4

Comments

The smallest k! with n prime factors occurs for n in A060250.

103!+1 = 27437*31084943*C153, so a(103) is unknown until this 153-digit composite is factored. a(104) = 4 and a(105) = 6. - Rick L. Shepherd, Jun 10 2003

Links

Amiram Eldar, Table of n, a(n) for n = 1..139

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

R. G. Wilson v, Explicit factorizations

Paul Leyland, Factors of n!+1.

Example

a(2)=2 because 4! + 1 = 25 = 5*5

Mathematica

a[q_] := Module[{x, n}, x=FactorInteger[q!+1]; n=Length[x]; Sum[Table[x[[i]][[2]], {i, n}][[j]], {j, n}]]
A054990[n_Integer] := PrimeOmega[n! + 1]; Table[A054990[n], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

Prog

(PARI) for(n=1, 64, print1(bigomega(n!+1), ", "))

Crossrefs

Cf. A000040 (prime numbers), A001359 (twin primes).

Cf. A038507, A054988, A054989, A054991, A054992.

Cf. A066856 (number of distinct prime divisors of n!+1), A084846 (mu(n!+1)).

Sequence in context: A330956 A190617 A068323 * A046921 A262954 A262813

Adjacent sequences: A054987 A054988 A054989 * A054991 A054992 A054993

Keyword

nonn,hard

Author

Arne Ring (arne.ring(AT)epost.de), May 30 2000

Extensions

More terms from Robert G. Wilson v, Mar 23 2001

More terms from Rick L. Shepherd, Jun 10 2003

Status

approved