login
a(n) = gcd(sigma(n), A156552(2*n)).
3

%I #12 Sep 11 2023 15:53:03

%S 1,3,1,7,3,1,1,15,13,1,3,1,1,1,3,31,3,3,1,3,1,1,3,1,1,1,1,1,5,1,1,63,

%T 3,1,1,1,1,5,7,1,3,3,1,3,3,1,3,1,1,3,9,1,1,1,1,1,1,1,3,3,1,1,1,127,1,

%U 1,1,3,3,1,1,3,1,1,1,1,3,3,5,3,1,7,3,1,1,1,1,1,1,13,1,3,1,1,1,1,1,9,3,1,1,1,1,1,1

%N a(n) = gcd(sigma(n), A156552(2*n)).

%H Antti Karttunen, <a href="/A365454/b365454.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = gcd(A000203(n), A156552(2*n)).

%F a(n) = A000203(n) / A365455(n) = A156552(2*n) / A365456(n).

%F For all n >= 0, a(2^n) = 2^(1+n) - 1 = A000225(1+n).

%o (PARI)

%o A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552

%o A365454(n) = gcd(sigma(n), A156552(2*n));

%Y Cf. A000203, A000225, A156552, A365455, A365456.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 10 2023