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 A054990 Number of prime divisors of n! + 1 (counted with multiplicity). 10
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A139514 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

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Last modified November 22 05:36 EST 2017. Contains 295076 sequences.