This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053026 #13 Feb 04 2025 07:15:40
%S A053026 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,
%T A053026 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,
%U A053026 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
%N A053026 Maximum power of 2 arising when A000005 is applied repeatedly to n!.
%C A053026 Unlike the iteration of Euler phi (A000010) 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.
%F A053026 a(n) = 2^A380802(n). - _Amiram Eldar_, Feb 04 2025
%e A053026 For n = 53, the iterations are {53!, 16174080000, 840, 32, 6, 4, 3, 2}, so a(53) = 32.
%e A053026 For n = 130, the iterations are {130!, 287298761874053529600, 38016, 64, 7, 2}, so a(130) = 64.
%e A053026 For n = 563, the iterations are {563!, 2875041108020454013464609906430286933482949481627276804096000000000, 77051520, 512, 10, 4, 3, 2}, so a(563) = 512.
%t A053026 Join[{1,2},Table[SelectFirst[Rest[NestWhileList[DivisorSigma[0,#]&,n!,#>2&]],IntegerQ[Log[2,#]]&],{n,3,100}]] (* _Harvey P. Dale_, Jul 02 2018 *)
%o A053026 (PARI) a(n) = {my(m = n!); while(1 << valuation(m, 2) != m, m = numdiv(m)); m;} \\ _Amiram Eldar_, Feb 04 2025
%Y A053026 Cf. A000005, A000142, A000010, A051953, A036450-A036459, A380802, A380803.
%K A053026 nonn
%O A053026 1,2
%A A053026 _Labos Elemer_, Feb 24 2000