A326195 Number of iterations of x -> A009195(x) needed to reach 1 when starting from x = n, where A009195(x) = gcd(x, phi(x)).

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 1, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 2, 1, 5, 1, 2, 1, 4, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 5, 2, 3, 1, 3, 1, 4, 2, 4, 2, 2, 1, 3, 1, 2, 3, 6, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 2, 3, 1, 3, 1, 5, 4, 2, 1, 4, 1, 2, 1, 4, 1, 3, 1, 3, 2, 2, 1, 6, 1, 3, 2, 4, 1, 2, 1, 4, 2

Offset: 1

Author

Antti Karttunen, Aug 24 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A009195, A326194, A326196.

Programs

Mathematica

Table[Length[NestWhileList[GCD[#,EulerPhi[#]]&,n,#>1&]]-1,{n,110}] (* Harvey P. Dale, Dec 21 2022 *)

PARI

A326195(n) = if(1==n,0,1+A326195(gcd(n,eulerphi(n))));

Formula

a(1) = 0; for n > 1, a(n) = 1 + a(A009195(n)).

a(n) < A326196(n).