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

1,6

Comments

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

Links

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

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A083662 A256405 A130149 * A261179 A066658 A005145

Adjacent sequences: A053043 A053044 A053045 * A053047 A053048 A053049

Keyword

nonn

Author

Labos Elemer, Feb 25 2000

Status

approved