A053046 - OEIS

%I #18 Aug 17 2024 09:01:35

%S 0,0,1,1,1,2,3,3,5,5,5,6,7,8,9,9,9,11,13,13,15,15,15,16,16,17,20,21,

%T 22,23,24,24,25,25,26,28,30,32,34,34,34,36,38,38,40,40,40,41,43,43,44,

%U 45,46,49,49,50,53,54,55,56,57,58,61,61,62,63,64,64,65,66,67,69,71,73,74

%N a(n) is the number of terms that are not powers of 2 among the iterates of the Euler phi function when it is iterated with initial value n!.

%C Non-powers of 2 arise at the beginning of iteration chains without interruption. Analogous to A053036.

%H Amiram Eldar, <a href="/A053046/b053046.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 1 + A053044(n) - A053045(n). - _R. J. Mathar_, Jan 09 2017

%e For n = 10, the initial value is 10! = 3628800 and the iteration chain is {3628800, 829440, 221184, 73728, 24576, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. Its length is 19 and there are 5 values that are not powers of 2: 10!, ..., 24576. Thus a(10) = 5.

%Y Cf. A000010, A000142, A048855, A053036, A053044, A053045.

%K nonn

%O 1,6

%A _Labos Elemer_, Feb 25 2000