A053046 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!.

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, 22, 23, 24, 24, 25, 25, 26, 28, 30, 32, 34, 34, 34, 36, 38, 38, 40, 40, 40, 41, 43, 43, 44, 45, 46, 49, 49, 50, 53, 54, 55, 56, 57, 58, 61, 61, 62, 63, 64, 64, 65, 66, 67, 69, 71, 73, 74

Offset: 1

Author

Labos Elemer, Feb 25 2000

Keywords

• nonn

Comments

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

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}. Its length is 19 and there are 5 values that are not powers of 2: 10!, ..., 24576. Thus a(10) = 5.
		

Links

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

Crossrefs

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

Formula

a(n) = 1 + A053044(n) - A053045(n). - R. J. Mathar, Jan 09 2017