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A195585 sigma(2*n^2) - sigma(n^2).

%I A195585 #15 Mar 17 2024 03:14:56
%S A195585 2,8,26,32,62,104,114,128,242,248,266,416,366,456,806,512,614,968,762,
%T A195585 992,1482,1064,1106,1664,1562,1464,2186,1824,1742,3224,1986,2048,3458,
%U A195585 2456,3534,3872,2814,3048,4758,3968,3446,5928,3786,4256,7502,4424,4514,6656,5602,6248,7982
%N A195585 sigma(2*n^2) - sigma(n^2).
%H A195585 Paul D. Hanna, <a href="/A195585/b195585.txt">Table of n, a(n) for n = 1..1000</a>
%F A195585 Equals the logarithmic derivative of A195584.
%F A195585 a(n) = A054785(n^2), where A054785 is the logarithmic derivative of A015128, which is the number of overpartitions of n.
%F A195585 Sum_{k=1..n} a(k) ~ c * n^3, where c = 7*zeta(3)/Pi^2 = 0.85255679763501158184... . - _Amiram Eldar_, Mar 17 2024
%e A195585 L.g.f.: L(x) = 2*x + 8*x^2/2 + 26*x^3/3 + 32*x^4/4 + 62*x^5/5 + 104*x^6/6 +...
%e A195585 where the g.f. of A195584 begins:
%e A195585 exp(L(x)) = 1 + 2*x + 6*x^2 + 18*x^3 + 42*x^4 + 102*x^5 + 238*x^6 +...
%t A195585 Table[DivisorSigma[1,2n^2]-DivisorSigma[1,n^2],{n,60}] (* _Harvey P. Dale_, May 05 2021 *)
%o A195585 (PARI) {a(n)=sigma(2*n^2)-sigma(n^2)}
%Y A195585 Cf. A195584, A215603, A054785, A015128, A002117.
%K A195585 nonn
%O A195585 1,1
%A A195585 _Paul D. Hanna_, Sep 20 2011