A336566 - OEIS

%I #6 Jul 28 2020 14:01:56

%S 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 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 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 a(n) = gcd(A336563(n), A336564(n)) = gcd(A057723(n)-n, n-A308135(n));

%H Antti Karttunen, <a href="/A336566/b336566.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = gcd(A336563(n), A336564(n)) = gcd(A057723(n)-n, n-A308135(n));

%o (PARI)

%o A007947(n) = factorback(factorint(n)[, 1]);

%o A057723(n) = { my(r=A007947(n)); (r*sigma(n/r)); };

%o A308135(n) = (sigma(n)-A057723(n));

%o A336563(n) = (A057723(n)-n);

%o A336564(n) = (n - A308135(n));

%o A336566(n) = gcd(A336563(n), A336564(n));

%Y Cf. A057723, A308135, A336563, A336564, A336565.

%Y 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 nonn

%O 1,3

%A _Antti Karttunen_, Jul 27 2020