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 A002128 MacMahon's generalized sum of divisors function. (Formerly M2784 N1119) 2
 1, 3, 9, 22, 42, 81, 140, 231, 351, 551, 783, 1134, 1546, 2142, 2835, 3758, 4818, 6237, 7826, 9885, 12159, 14974, 18261, 22113, 26511, 31668, 37611, 44149, 52074, 60660, 70569, 81396, 94311, 107317, 123879, 140049, 160154, 179949, 204867, 228137 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS John Cerkan, Table of n, a(n) for n = 6..10000 G. E. Andrews and S. C. F. Rose, MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms, arXiv:1010.5769 [math.NT], 2010. P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1921), 75-113; Coll. Papers II, pp. 303-341. FORMULA G.f.: (t(1)^3-3*t(1)*t(2)+2*t(3))/6 where t(i) = Sum(x^(n*i)/(1-x^n)^(2*i),n=1..inf), i=1..3. - Vladeta Jovovic, Sep 21 2007 G.f.: (Sum_{k>=0} (-1)^k * (2*k + 1) * binomial( k+3, 6) * x^( k*(k+1) / 2 )) / (-7  * Sum_{k>=0} (-1)^k * (2*k + 1) * x^( k*(k+1) / 2 )). - Michael Somos, Jan 10 2012 EXAMPLE x^6 + 3*x^7 + 9*x^8 + 22*x^9 + 42*x^10 + 81*x^11 + 140*x^12 + 231*x^13 + ... PROG (PARI) {a(n) = if( n<1, 0, (3*sigma(n, 5) + (-30*n + 50)*sigma(n, 3) + (40*n^2 - 100*n + 37)*sigma(n)) / 1920)} /* Michael Somos, Jan 10 2012 */ CROSSREFS A diagonal of A060043. Sequence in context: A318807 A063586 A131477 * A064808 A223718 A217882 Adjacent sequences:  A002125 A002126 A002127 * A002129 A002130 A002131 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Naohiro Nomoto, Jan 24 2002 More terms from Vladeta Jovovic, Sep 21 2007 STATUS approved

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Last modified April 19 08:06 EDT 2021. Contains 343110 sequences. (Running on oeis4.)