A053048 a(n) is the number of terminal iterations applied to powers of 2 arising in the iterations of the Euler phi function with initial value n!.

0, 1, 1, 3, 5, 6, 7, 10, 10, 13, 16, 18, 20, 22, 24, 28, 32, 33, 34, 38, 39, 43, 47, 50, 54, 57, 57, 60, 63, 66, 69, 74, 77, 82, 85, 87, 89, 91, 93, 98, 103, 105, 107, 112, 114, 119, 124, 128, 130, 135, 139, 143, 147, 148, 153, 157, 158, 162, 166, 170, 174, 178, 179

Offset: 1

Author

Labos Elemer, Feb 25 2000

Keywords

• nonn

Examples

			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}. The first power of 2 is 8192, after which phi is applied 13 additional times to reach the stationary value 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000142, A048855, A053039, A053047.

Programs

Mathematica

a[n_] := Max@ IntegerExponent[ FixedPointList[ EulerPhi, n!], 2]; Array[a, 63] (* Giovanni Resta, May 30 2018 *)

Formula

a(n) = log_2(A053047(n)). - Amiram Eldar, Aug 17 2024