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A049115 If n is a power of 2, then a(n) = 0; otherwise, a(n) is the number of iterations of the Euler phi function that must be repeatedly applied to n to reach 1. 6
0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 2, 1, 2, 2, 1, 0, 1, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 1, 2, 0, 2, 1, 2, 2, 3, 3, 2, 1, 2, 2, 3, 2, 2, 3, 4, 1, 3, 2, 1, 2, 3, 3, 2, 2, 3, 3, 4, 1, 2, 2, 3, 0, 2, 2, 3, 1, 3, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 1, 4, 2, 3, 2, 1, 3, 3, 2, 3, 2, 3, 3, 2, 4, 3, 1, 2, 3, 2, 2, 3, 1, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

a(n) = A227944(n) if n is not a power of 2. - Eric M. Schmidt, Oct 13 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

The smallest x so that Nest[ EulerPhi, n, x ] = 2^w is just achieved.

EXAMPLE

If n is a power of 2, then a(n)=0 by definition. If n = 59049, then {59049, 39366, 13122, 4374, 1458, 486, 54, 18, 6, 2, 1}. This phi-sequence has a length of 12 and includes 10 numbers that are not powers of 2, so a(59049) = 8.

MATHEMATICA

Table[If[IntegerQ@ Log2@ n, 0, -1 + Length@ NestWhileList[EulerPhi, n, ! IntegerQ@ Log2@ # &]], {n, 105}] (* Michael De Vlieger, Aug 01 2017 *)

CROSSREFS

Cf. A000010, A057716, A227944.

Sequence in context: A039701 A025822 A051585 * A294204 A329697 A029367

Adjacent sequences:  A049112 A049113 A049114 * A049116 A049117 A049118

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified July 31 04:58 EDT 2021. Contains 346367 sequences. (Running on oeis4.)