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A053099 When the Euler phi function is iterated with initial value A002110(n) = n-th primorial, a(n) = exponent of largest power of 2 arising in the iteration. 0
1, 1, 3, 4, 7, 9, 13, 14, 18, 21, 24, 26, 31, 33, 38, 42, 46, 50, 54, 58, 61, 64, 70, 76, 81, 87, 92, 97, 99, 104, 106, 111, 118, 123, 127, 132, 136, 137, 144, 148, 155, 159, 163, 169, 173, 177, 181, 184, 190, 193, 199, 205, 211, 218, 226, 232, 238, 241, 247, 253 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Analogous to A053048.

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

n=6, A002110(6)=30030; the corresponding iteration chain is {30030, 5760, 1536, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. The first power of 2 is the 4th item after 3 iterations. It is 512, therefore a(6) = log_2(512) = 9 and a(6) + 1 = 10 iterations is needed to reach the stationary value = 1. a(6)=512.

MATHEMATICA

a[n_] := Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[ Range@ n]], 2]; Array[a, 60] (* Giovanni Resta, May 30 2018 *)

CROSSREFS

Cf. A000010, A002110.

Sequence in context: A005539 A253060 A203623 * A073273 A247835 A072441

Adjacent sequences:  A053096 A053097 A053098 * A053100 A053101 A053102

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 28 2000

STATUS

approved

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Last modified October 19 14:54 EDT 2019. Contains 328223 sequences. (Running on oeis4.)