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 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 (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 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

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Last modified January 24 16:44 EST 2020. Contains 331209 sequences. (Running on oeis4.)