A053097 When the Euler phi function is iterated with initial value A002110(n) = primorial, a(n) = number of powers of 2 among iterates.

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

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: A326630 A317810 A308954 * A331443 A367411 A367684

Adjacent sequences: A053094 A053095 A053096 * A053098 A053099 A053100

Keyword

nonn

Author

Labos Elemer, Feb 28 2000

Status

approved