A377957 - OEIS

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..87.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A000203, A001065, A009194.

Sequence in context: A154718 A334424 A021537 * A208934 A196620 A200598

Adjacent sequences: A377954 A377955 A377956 * A377958 A377959 A377960

KEYWORD

nonn,new

AUTHOR

Ctibor O. Zizka, Nov 12 2024

STATUS

approved