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

Offset: 1

Author

Labos Elemer, Sep 22 2004

Keywords

• nonn
• more

Examples

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

Crossrefs

Cf. A002110, A051953, A053475, A098115.

Programs

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 *)

PARI

a(n) = {my(p = prod(i=1, n, prime(i)), c = 1); while(p > 0, c++; p -= eulerphi(p)); c;} \\ Amiram Eldar, Nov 19 2024

Formula

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

Extensions

More terms from Robert G. Wilson v, Sep 22 2004

a(37)-a(54) from Amiram Eldar, Nov 19 2024