A378929 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.

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, 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, 3, 0, 1, 1, 1, 0, 0, 4, 1, 3, 1, 3, 1, 0, 1, 2, 1, 0, 3, 2

Offset

1,4

Comments

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

Links

Viliam Furík, Table of n, a(n) for n = 1..10000

Mathematica

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 *)

Crossrefs

Cf. A000005, A378930.

Sequence in context: A346061 A053382 A031253 * A291624 A291635 A308243

Adjacent sequences: A378926 A378927 A378928 * A378930 A378931 A378932

Keyword

nonn

Author

Viliam Furík, Dec 11 2024

Status

approved