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
Keywords
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
a[n_] := 1 + Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[Range[n]]], 2]; Array[a, 60] (* Giovanni Resta, May 30 2018 *)
-
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