cp's OEIS Frontend

A327164 Number of iterations of x -> gcd(usigma(x),x) needed to reach a fixed point, where usigma is the sum of unitary divisors of n (A034448).

%I A327164 #7 Sep 05 2019 20:49:24
%S A327164 0,1,1,1,1,0,1,1,1,2,1,2,1,2,2,1,1,1,1,3,1,2,1,3,1,2,1,2,1,1,1,1,2,2,
%T A327164 1,2,1,2,1,2,1,1,1,2,3,2,1,2,1,2,2,2,1,1,1,2,1,2,1,0,1,2,1,1,1,1,1,2,
%U A327164 2,2,1,2,1,2,1,2,1,1,1,2,1,2,1,2,1,2,2,2,1,0,2,2,1,2,2,3,1,2,2,3,1,1,1,2,2
%N A327164 Number of iterations of x -> gcd(usigma(x),x) needed to reach a fixed point, where usigma is the sum of unitary divisors of n (A034448).
%H A327164 Antti Karttunen, <a href="/A327164/b327164.txt">Table of n, a(n) for n = 1..16384</a>
%H A327164 Antti Karttunen, <a href="/A327164/a327164.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%o A327164 (PARI)
%o A327164 A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
%o A327164 A323166(n) = gcd(n, A034448(n));
%o A327164 A327164(n) = { my(u=A323166(n)); if(u==n,0,1+A327164(u)); }
%Y A327164 Cf. A034448, A323166, A327158 (positions of zeros).
%Y A327164 Cf. also A326194.
%K A327164 nonn
%O A327164 1,10
%A A327164 _Antti Karttunen_, Aug 28 2019