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%I #20 Sep 15 2023 10:32:55
%S 1,2,4,8,14,24,40,56,84,122,168,232,312,408,528,672,865,1078,1336,
%T 1648,2002,2424,2912,3472,4116,4872,5744,6648,7752,8976,10304,11872,
%U 13566,15424,17556,19896,22414,25256,28336,31584,35462,39482,43728,48664
%N Generalized sum of divisors function: third diagonal of A060047.
%H Seiichi Manyama, <a href="/A060046/b060046.txt">Table of n, a(n) for n = 9..10000</a>
%H G. E. Andrews and S. C. F. Rose, <a href="http://arxiv.org/abs/1010.5769">MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms</a>, arXiv:1010.5769 [math.NT], 2010.
%H P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.75">Divisors of numbers and their continuations in the theory of partitions</a>, Proc. London Math. Soc., 19 (1919), 75-113; Coll. Papers II, pp. 303-341.
%F G.f.: (t(1)^3-3*t(1)*t(2)+2*t(3))/6 where t(i) = Sum((x^(2*n-1)/(1-x^(2*n-1))^2)^i,n=1..inf), i=1..3. - _Vladeta Jovovic_, Sep 21 2007
%F G.f.: -(1/3) * ( Sum_{k>=3} (-1)^k * k * binomial(k+2,5) * q^(k^2) ) / ( 1 + 2 * Sum_{k>=1} (-q)^(k^2) ). - _Seiichi Manyama_, Sep 15 2023
%Y Cf. A015128.
%K nonn,easy
%O 9,2
%A _N. J. A. Sloane_, Mar 19 2001
%E More terms from _Naohiro Nomoto_, Jan 24 2002
%E More terms from _Vladeta Jovovic_, Sep 21 2007
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