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A054990
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Number of prime divisors of n! + 1 (counted with multiplicity).
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11
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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
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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EXAMPLE
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a(2)=2 because 4! + 1 = 25 = 5*5
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MATHEMATICA
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a[q_] := Module[{x, n}, x=FactorInteger[q!+1]; n=Length[x]; Sum[Table[x[[i]][[2]], {i, n}][[j]], {j, n}]]
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PROG
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(PARI) for(n=1, 64, print1(bigomega(n!+1), ", "))
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CROSSREFS
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Cf. A066856 (number of distinct prime divisors of n!+1), A084846 (mu(n!+1)).
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KEYWORD
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nonn,hard
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AUTHOR
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Arne Ring (arne.ring(AT)epost.de), May 30 2000
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EXTENSIONS
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STATUS
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approved
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