

A053048


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


1



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
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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: A163621 A124194 A055597 * A154663 A028983 A232682
Adjacent sequences: A053045 A053046 A053047 * A053049 A053050 A053051


KEYWORD

nonn


AUTHOR

Labos Elemer, Feb 25 2000


STATUS

approved



