A378929 - OEIS

%I #15 Dec 16 2024 17:27:38

%S 0,1,1,3,1,0,1,2,2,0,1,2,1,0,3,4,1,2,1,4,3,0,1,2,1,0,4,4,1,3,1,6,3,0,

%T 1,4,1,0,3,2,1,3,1,4,4,0,1,5,1,0,3,4,1,4,1,2,3,0,1,2,1,0,4,8,1,3,1,4,

%U 3,0,1,1,1,0,0,4,1,3,1,3,1,0,1,2,1,0,3,2

%N Number of steps it takes for the chain of f(n) = n * d(n) / gcd(n, d(n))^2 to reach a cycle from a starting number n.

%C It is conjectured that every number n eventually ends up in a cycle.

%H Viliam Furík, <a href="/A378929/b378929.txt">Table of n, a(n) for n = 1..10000</a>

%t f[n_] := Module[{d = DivisorSigma[0, n]}, n*d/GCD[n, d]^2]; a[n_] := Module[{s = NestWhileList[f, n, UnsameQ, All]}, FirstPosition[s, s[[-1]]][[1]] - 1]; Array[a, 100] (* _Amiram Eldar_, Dec 16 2024 *)

%Y Cf. A000005, A378930.

%K nonn

%O 1,4

%A _Viliam Furík_, Dec 11 2024