A060046 Generalized sum of divisors function: third diagonal of A060047.

1, 2, 4, 8, 14, 24, 40, 56, 84, 122, 168, 232, 312, 408, 528, 672, 865, 1078, 1336, 1648, 2002, 2424, 2912, 3472, 4116, 4872, 5744, 6648, 7752, 8976, 10304, 11872, 13566, 15424, 17556, 19896, 22414, 25256, 28336, 31584, 35462, 39482, 43728, 48664

Offset

9,2

Links

Seiichi Manyama, Table of n, a(n) for n = 9..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 (1919), 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^(2*n-1)/(1-x^(2*n-1))^2)^i,n=1..inf), i=1..3. - Vladeta Jovovic, Sep 21 2007

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

Crossrefs

Cf. A015128.

Sequence in context: A344741 A280874 A243815 * A053801 A091778 A053802

Adjacent sequences: A060043 A060044 A060045 * A060047 A060048 A060049

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 19 2001

Extensions

More terms from Naohiro Nomoto, Jan 24 2002

More terms from Vladeta Jovovic, Sep 21 2007

Status

approved