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A053026
Maximal power of 2 arising when A000005 is applied repeatedly to n!.
0
1, 2, 4, 8, 16, 8, 4, 4, 4, 16, 8, 8, 8, 8, 8, 2, 8, 4, 8, 4, 4, 4, 4, 4, 4, 4, 16, 16, 4, 16, 8, 16, 4, 4, 16, 4, 4, 2, 4, 16, 8, 16, 16, 4, 8, 8, 4, 8, 8, 16, 8, 8, 32, 32, 4, 32, 4, 4, 8, 4, 2, 32, 2, 8, 4, 8, 4, 8, 8, 8, 8, 2, 8, 8, 8, 32, 32, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 32, 8, 8, 2, 4, 2, 4, 8
OFFSET
1,2
COMMENTS
Unlike the iteration of EulerPhi(A000005) or Cototient(A051953) functions, here the emerging powers of 2 are not accumulated at the terminal phase of iteration sequence. Non-2-powers can be intercalated.
EXAMPLE
n=53, the iterates are {53!,16174080000,840,32,6,4,3,2}, so a(53)=32, n=130, the iterates are {130!,287298761874053529600,38016,64,7,2}, so a(130)=64, n=563, the iterates are {563!,2875041108020454013464609906430286933482949481627276804096000000000, 77051520,512,10,4,3,2}, so a(563)=512.
MATHEMATICA
Join[{1, 2}, Table[SelectFirst[Rest[NestWhileList[DivisorSigma[0, #]&, n!, #>2&]], IntegerQ[Log[2, #]]&], {n, 3, 100}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 02 2018 *)
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 24 2000
STATUS
approved