A098202 - OEIS

A098202

a(n) is the length of the iteration trajectory when the cototient function (A051953) is applied to the n-th primorial number (A002110(n)).

3, 5, 8, 12, 18, 20, 31, 32, 41, 43, 61, 65, 80, 77, 95, 125, 131, 125, 157, 173, 140, 192, 195, 221, 213, 212, 261, 269, 277, 300, 296, 321, 336, 329, 358, 367, 379, 405, 428, 439, 438, 464, 477, 493, 506, 454, 491, 542, 564, 588, 543, 600, 639, 660

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..54.

FORMULA

a(n) = A053475(A002110(n)). - Robert G. Wilson v, Sep 22 2004

EXAMPLE

For n = 3: list = {30,22,12,8,4,2,1,0}, a(4) = 8.

MATHEMATICA

g[x_] := x - EulerPhi[x]; f[x_] := Length[ FixedPointList[g, x]] - 1; q[x_] := Product[ Prime[j], {j, x}]; Table[ f[ q[n]], {n, 33}]

a[n_] := Length@ NestWhileList[(# - EulerPhi[#])&, Times @@ Prime[Range[n]], # > 0 &]; Array[a, 30] (* Amiram Eldar, Nov 19 2024 *)