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%I #11 Sep 11 2023 15:52:53
%S 1,1,5,1,3,11,17,1,1,19,11,23,65,35,7,1,43,9,257,13,37,67,171,47,25,
%T 131,29,71,205,43,2049,1,23,259,41,55,4097,103,19,79,2731,25,16385,45,
%U 15,1027,10923,95,49,17,29,263,65537,59,73,143,517,2051,43691,29,262145,4099,77,1,137,139,524289,173,343,83
%N a(n) = A156552(2*n) / gcd(sigma(n), A156552(2*n)).
%C Denominator of ratio sigma(n) / A156552(2*n).
%H Antti Karttunen, <a href="/A365456/b365456.txt">Table of n, a(n) for n = 1..8192</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) = A156552(2*n) / A365454(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 A365456(n) = { my(u=A156552(2*n)); (u/gcd(u, sigma(n))); };
%Y Cf. A000203, A156552, A365454, A365455 (numerators), A365457.
%K nonn,frac
%O 1,3
%A _Antti Karttunen_, Sep 10 2023
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