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A054990
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Number of prime divisors of n! + 1 (counted with multiplicity).
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10
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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; internal format)
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OFFSET
| 1,4
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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 (rshepherd2(AT)hotmail.com), Jun 10 2003
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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.
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EXAMPLE
| a(2)=2 because 4! + 1 = 25 = 5*5
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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}] (* From Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
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PROG
| (PARI) for(n=1, 64, print1(bigomega(n!+1), ", "))
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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 A188794 A161966
Adjacent sequences: A054987 A054988 A054989 * A054991 A054992 A054993
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KEYWORD
| nonn,hard
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AUTHOR
| Arne Ring (arne.ring(AT)epost.de), May 30 2000
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EXTENSIONS
| More terms from Robert G. Wilson V (rgwv(AT)rgwv.com), Mar 23 2001
More terms from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 10 2003
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