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A053097 When the Euler phi function is iterated with initial value A002110(n) = primorial, a(n) = number of powers of 2 among iterates. 0
2, 2, 4, 5, 8, 10, 14, 15, 19, 22, 25, 27, 32, 34, 39, 43, 47, 51, 55, 59, 62, 65, 71, 77, 82, 88, 93, 98, 100, 105, 107, 112, 119, 124, 128, 133, 137, 138, 145, 149, 156, 160, 164, 170, 174, 178, 182, 185, 191, 194, 200, 206, 212, 219, 227, 233, 239, 242, 248, 254 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

n=8, A002110(8)=9699690; the corresponding iteration chain is {9699690, 1658880, 442368, 147456, 49152, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. Its length is 20 of which 15 terms are powers of 2: a(8)=15. Its length is 17, so the required number of iterations is a(7)=16.

MATHEMATICA

a[n_] := 1 + Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[Range[n]]], 2]; Array[a, 60] (* Giovanni Resta, May 30 2018 *)

CROSSREFS

Analogous to A053035, A053045.

Cf. A000010, A002110.

Sequence in context: A183564 A222707 A317810 * A035946 A303939 A323530

Adjacent sequences:  A053094 A053095 A053096 * A053098 A053099 A053100

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 28 2000

STATUS

approved

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Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)