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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

For n=8, A002110(8) = 9699690 and 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 and it has 15 terms that are powers of 2. Thus a(8) = 15.

Mathematica

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

Prog

(PARI) ispow2(n) = n >> valuation(n, 2) == 1;
a(n) = {my(p = vecprod(primes(n))); while(!ispow2(p), p = eulerphi(p)); valuation(p, 2) + 1; } \\ Amiram Eldar, Aug 17 2024

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