A333609 The number of iterations of the infinitary totient function iphi (A091732) required to reach from n to 1.

0, 1, 2, 3, 4, 2, 3, 3, 4, 4, 5, 3, 4, 3, 4, 5, 6, 4, 5, 4, 4, 5, 6, 3, 4, 4, 6, 5, 6, 4, 5, 5, 5, 6, 4, 4, 5, 5, 4, 4, 5, 4, 5, 5, 6, 6, 7, 5, 6, 4, 6, 5, 6, 6, 5, 5, 5, 6, 7, 4, 5, 5, 6, 7, 6, 5, 6, 6, 6, 4, 5, 4, 5, 5, 6, 7, 5, 4, 5, 5, 6, 5, 6, 5, 8, 5, 6

Offset: 1

Author

Amiram Eldar, Mar 28 2020

Keywords

• nonn

Examples

			a(6) = 2 since there are 2 iterations from 6 to 1: iphi(6) = 2 and iphi(2) = 1.
		

Links

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

Crossrefs

Cf. A003434, A049865, A091732.

Programs

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], 1])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1); a[n_] := Length @ NestWhileList[iphi, n, # != 1 &] - 1; Array[a, 100]