%I M2770 N1114 #22 Sep 27 2017 02:32:55

%S 1,3,9,15,30,45,67,99,135,175,231,306,354,465,540,681,765,945,1040,

%T 1305,1386,1695,1779,2205,2290,2754,2835,3438,3480,4185,4272,5076,

%U 5004,6100,5985,7155,7154,8325,8190,9840,9471,11241,11055,12870,12420,14911

%N MacMahon's generalized sum of divisors function.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H John Cerkan, <a href="/A002127/b002127.txt">Table of n, a(n) for n = 3..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="http://dx.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 (1921), 75-113; Coll. Papers II, pp. 303-341.

%H S. Rose, <a href="http://mathoverflow.net/questions/41457/">What literature is known about MacMahon's generalized sum-of-divisors function?</a>

%F G.f.: (Sum_{k>=0} (-1)^k * (2*k + 1) * binomial( k+2, 4) * x^( k*(k+1) / 2 )) / (5 * Sum_{k>=0} (-1)^k * (2*k + 1) * x^( k*(k+1) / 2 )). - _Michael Somos_, Jan 10 2012

%e x^3 + 3*x^4 + 9*x^5 + 15*x^6 + 30*x^7 + 45*x^8 + 67*x^9 + 99*x^10 + ...

%o (PARI) {a(n) = if( n<1, 0, ( sigma( n, 3) - (2*n - 1) * sigma(n) ) / 8)} /* _Michael Somos_, Jan 10 2012 */

%Y A diagonal of A060043.

%K nonn,easy

%O 3,2

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Nov 11 2001