%I #12 Jun 15 2023 20:06:35
%S 0,1,2,2,3,2,3,0,3,3,4,3,4,3,1,1,2,3,4,1,4,4,5,1,2,4,0,4,5,1,2,2,2,2,
%T 2,4,5,4,2,2,3,4,5,2,2,5,6,2,5,2,3,2,3,4,3,2,5,5,6,2,3,2,5,0,3,2,3,3,
%U 3,2,3,2,3,5,3,5,3,2,3,3,5,3,4,2,1,5,3
%N Number of iterations of phi(x) at n needed to reach a cube.
%t a[n_] := a[n] = If[IntegerQ[Surd[n, 3]], 0, a[EulerPhi[n]] + 1]; Array[a, 100] (* _Amiram Eldar_, Jun 14 2023 *)
%o (Python)
%o from sympy import totient, integer_nthroot
%o def a(n):
%o x = n
%o c = 0
%o while not integer_nthroot(x,3)[1]:
%o x = totient(x)
%o c += 1
%o return c
%o (PARI) a(n) = my(nb=0); while(!ispower(n, 3), n=eulerphi(n); nb++); nb; \\ _Michel Marcus_, Jun 15 2023
%Y Cf. A000010, A363612, A003434.
%K nonn
%O 1,3
%A _DarĂo Clavijo_, Jun 14 2023