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A002132 Generalized sum of divisors function.
(Formerly M1096 N0418)
4
1, 2, 4, 8, 14, 18, 28, 40, 52, 70, 88, 104, 140, 168, 196, 240, 278, 320, 380, 440, 504, 562, 644, 720, 808, 910, 1000, 1120, 1240, 1360, 1488, 1600, 1789, 1938, 2100, 2296, 2452, 2660, 2880, 3080, 3292, 3542, 3784, 4048, 4400, 4572, 4868, 5280, 5502, 5850 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,2
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
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.: (1/2) * ( Sum_{k>=2} (-1)^k * k * binomial(k+1,3) * q^(k^2) ) / ( 1 + 2 * Sum_{k>=1} (-q)^(k^2) ). - Seiichi Manyama, Sep 15 2023
CROSSREFS
A diagonal of A060047.
Cf. A015128.
Sequence in context: A188629 A084621 A248379 * A294065 A248845 A370047
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Naohiro Nomoto and Vladeta Jovovic, Jan 25 2002
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)