cp's OEIS Frontend

A336566 a(n) = gcd(A336563(n), A336564(n)) = gcd(A057723(n)-n, n-A308135(n)).

%I A336566 #8 Jun 01 2025 19:58:22
%S A336566 1,1,2,1,4,0,6,1,1,2,10,2,12,4,6,1,16,3,18,2,10,8,22,6,1,10,2,14,28,
%T A336566 12,30,1,18,14,22,1,36,16,22,10,40,12,42,2,3,20,46,14,1,1,30,2,52,12,
%U A336566 38,2,34,26,58,6,60,28,1,1,46,12,66,2,42,4,70,3,72,34,1,2,58,12,78,2,1,38,82,14,62,40,54,2,88
%N A336566 a(n) = gcd(A336563(n), A336564(n)) = gcd(A057723(n)-n, n-A308135(n)).
%H A336566 Antti Karttunen, <a href="/A336566/b336566.txt">Table of n, a(n) for n = 1..20000</a>
%F A336566 a(n) = gcd(A336563(n), A336564(n)) = gcd(A057723(n)-n, n-A308135(n));
%o A336566 (PARI)
%o A336566 A007947(n) = factorback(factorint(n)[, 1]);
%o A336566 A057723(n) = { my(r=A007947(n)); (r*sigma(n/r)); };
%o A336566 A308135(n) = (sigma(n)-A057723(n));
%o A336566 A336563(n) = (A057723(n)-n);
%o A336566 A336564(n) = (n - A308135(n));
%o A336566 A336566(n) = gcd(A336563(n), A336564(n));
%Y A336566 Cf. A057723, A308135, A336563, A336564, A336565.
%Y A336566 Differs from A326144 at the positions given by A336555, for the first time at n=45, where a(45) = 3, while A326144(45) = 6.
%K A336566 nonn
%O A336566 1,3
%A A336566 _Antti Karttunen_, Jul 27 2020