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A053025
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Number of iterations of the number of divisors function (A000005) required to reach a fixed point (1 or 2) when started at n!.
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2
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1, 1, 4, 5, 4, 6, 7, 7, 7, 5, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 6, 6, 8, 6, 7, 6, 7, 8, 6, 8, 7, 5, 7, 6, 8, 6, 6, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 7, 8, 8, 7, 8, 8, 8, 8, 8
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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For n = 108, a(108) = 9 because the sequence of iterates is {108!, 798687560466432000, 7920, 60, 12, 6, 4, 3, 2}, and its length is 9.
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MATHEMATICA
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a[n_] := -1 + Length @ FixedPointList[DivisorSigma[0, #] &, n!]; Array[a, 100] (* Amiram Eldar, Aug 17 2024 *)
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PROG
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(PARI) a(n) = {my(f = n!, c = 1); while(f > 2, f = numdiv(f); c++); c; } \\ Amiram Eldar, Aug 17 2024
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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