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

1,1

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 *)

Prog

(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

Crossrefs

Cf. A002110, A051953, A053475, A098115.

Sequence in context: A265061 A265062 A265063 * A164653 A001973 A248374

Adjacent sequences: A098199 A098200 A098201 * A098203 A098204 A098205

Keyword

nonn,more

Author

Labos Elemer, Sep 22 2004

Extensions

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

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

Status

approved