A326194 - OEIS

%I #10 Aug 24 2019 11:57:56

%S 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,

%T 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,

%U 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

%N 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)).

%H Antti Karttunen, <a href="/A326194/b326194.txt">Table of n, a(n) for n = 1..65537</a>

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

%F a(n) < A326196(n).

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

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

%K nonn

%O 1,10

%A _Antti Karttunen_, Aug 24 2019