A053048 EulerPhi is iterated with initial value n!; a(n) = number of terminal iterations applied to powers of 2 arising in the iteration.

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

1,4

Links

Table of n, a(n) for n=1..63.

Example

For n=10, initial value = 3628800; 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 was applied 13 more times to reach the stationary value 1.

Mathematica

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

Crossrefs

Cf. A000010, A000142, A048855, A053039.

Sequence in context: A124194 A359506 A055597 * A154663 A028983 A232682

Adjacent sequences: A053045 A053046 A053047 * A053049 A053050 A053051

Keyword

nonn

Author

Labos Elemer, Feb 25 2000

Status

approved