

A054990


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


11



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
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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 153digit 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). Also 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



