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

1,10

Links

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

Formula

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

a(n) < A326196(n).

Prog

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

Crossrefs

Cf. A000203, A007691 (positions of zeros), A009194, A326195, A326196.

Sequence in context: A306717 A195969 A023518 * A331251 A309858 A022921

Adjacent sequences: A326191 A326192 A326193 * A326195 A326196 A326197

Keyword

nonn

Author

Antti Karttunen, Aug 24 2019

Status

approved