login
The first (largest) power of 2 arising in the iteration-sequence when A051953 (the cototient function) is repeatedly applied starting with n!.
2

%I #13 Aug 17 2017 11:58:13

%S 1,2,4,16,32,128,512,4096,16384,2048,8192,65536,16384,65536,8388608,

%T 134217728,8388608,8388608,16777216,2097152,8388608,268435456,

%U 4398046511104,70368744177664,67108864,67108864,67108864,68719476736

%N The first (largest) power of 2 arising in the iteration-sequence when A051953 (the cototient function) is repeatedly applied starting with n!.

%e For n = 10, initial value = 10! = 3628800; after the following initial terms {3628800, 2799360, 2052864, 1430784, 974592, 656640, 490752, 329472, 237312, 158976, 108288, 72960, 54528, 36608, 21248, 10752, 7680, 5632, 3072, ...}, the first power of 2 is 2048 = cototient(3072). Therefore a(10) = 2048.

%t Table[NestWhile[# - EulerPhi@ # &, n!, ! IntegerQ@ Log2@ # &], {n, 28}] (* _Michael De Vlieger_, Aug 15 2017 *)

%Y Cf. A051953, A053475, A053039.

%K nonn

%O 1,2

%A _Labos Elemer_, Feb 24 2000