A326194 Number of iterations of x -> A009194(x) needed to reach a fixed point when starting from x = n, where A009194(x) = gcd(x, sigma(x)).

0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 0, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 3, 2, 2, 1, 2, 2, 3, 1, 1, 2, 1, 1, 1, 1, 2, 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. A000203, A007691 (positions of zeros), A009194, A326195, A326196.

Programs

PARI

A326194(n) = { my(u=gcd(n,sigma(n))); if(u==n,0,1+A326194(u)); };

Formula

If gcd(n,sigma(n)) = n, then a(n) = 0, otherwise a(n) = 1 + a(gcd(n,sigma(n))).

a(n) < A326196(n).