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.

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

Offset

1,3

Comments

Analogous to A053048.

Links

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

Formula

a(n) = log_2(A053098(n)). - Amiram Eldar, Nov 19 2024

Example

For 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.

Mathematica

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

Prog

(PARI) a(n) = {my(p = prod(i=1, n, prime(i))); while(p >> valuation(p, 2) > 1, p = eulerphi(p)); valuation(p, 2); } \\ Amiram Eldar, Nov 19 2024

Crossrefs

Cf. A000010, A002110, A053048, A053098.

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