|
%I #12 Apr 07 2020 17:10:41
%S 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,
%T 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,
%U 6,4,5,4,5,5,6,7,5,4,5,5,6,5,6,5,8,5,6
%N The number of iterations of the infinitary totient function iphi (A091732) required to reach from n to 1.
%H Amiram Eldar, <a href="/A333609/b333609.txt">Table of n, a(n) for n = 1..10000</a>
%e a(6) = 2 since there are 2 iterations from 6 to 1: iphi(6) = 2 and iphi(2) = 1.
%t 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]
%Y Cf. A003434, A049865, A091732.
%K nonn
%O 1,3
%A _Amiram Eldar_, Mar 28 2020
|
