A377957 The number of iterations of the map x -> x + A001065(x) if A009194(x) = 1, x -> x / A009194(x) otherwise, starting from n, until reaching 1.

0, 8, 7, 6, 2, 1, 5, 4, 8, 3, 9, 8, 7, 6, 3, 14, 3, 2, 5, 4, 13, 10, 10, 9, 14, 8, 8, 1, 4, 3, 13, 12, 10, 4, 10, 9, 7, 6, 7, 7, 7, 6, 11, 10, 4, 11, 10, 9, 10, 14, 4, 9, 10, 9, 11, 6, 9, 5, 4, 3, 15, 14, 11, 14, 9, 10, 6, 5, 11, 11, 11, 10, 9, 8, 15, 6, 6, 8, 9, 8, 12, 8, 9, 8, 10, 12, 5

Offset: 1

Author

Ctibor O. Zizka, Nov 12 2024

Keywords

• nonn

Examples

			For n = 2 there are a(2) = 8 iterations to reach 1: 2 -> 3 -> 4 -> 7 -> 8 -> 15 -> 5 -> 6 -> 1.
For n = 9 there are a(9) = 8 iterations to reach 1: 9 -> 13 -> 14 -> 7 -> 8 -> 15 -> 5 -> 6 -> 1.
		

Crossrefs

Cf. A000203, A001065, A009194.

Programs

Mathematica

f[n_] := Module[{s = DivisorSigma[1, n], g}, g = GCD[n, s]; If[g == 1, s, n/g]]; a[n_] := -1 + Length@ NestWhileList[f, n, # > 1 &]; Array[a, 100] (* Amiram Eldar, Nov 12 2024 *)