A053026 Maximal power of 2 arising when A000005 is applied repeatedly to n!.

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.

Links

Table of n, a(n) for n=1..95.

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 *)

Crossrefs

A000005, A000142, A000010, A051953, A036450-A036459.

Sequence in context: A228846 A070336 A348433 * A119318 A082953 A009289

Adjacent sequences: A053023 A053024 A053025 * A053027 A053028 A053029

Keyword

nonn

Author

Labos Elemer, Feb 24 2000

Status

approved