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A002130 Generalized sum of divisors function.
(Formerly M2238 N0888)
2
1, -1, 1, 3, -2, 1, -5, 23, -25, 27, -49, 74, -62, 85, -132, 165, -195, 229, -240, 325, -374, 379, -469, 553, -590, 746, -805, 854, -1000, 1085, -1168, 1284, -1396, 1668, -1767, 1815, -2030, 2297, -2450, 2480, -2849, 3293, -3113, 3278, -3772, 4091, -4230, 4213, -4830, 5607, -5499, 5430, -6018, 6922, -6880 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,4

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

Table of n, a(n) for n=3..57.

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)^2-t(2))/2 where t(i) = Sum(x^(n*i)/(1+x^n)^(2*i),n=1..inf), i=1..2. - Vladeta Jovovic, Sep 21 2007

MATHEMATICA

terms = 55; offset = 3; t[i_] := Sum[x^(n*i)/(1 + x^n)^(2*i), {n, 1, terms + 5}]; s = Series[(t[1]^2 - t[2])/2, {x, 0, terms + 5 }]; A002130 = CoefficientList[s, x][[offset + 1 ;; terms + offset]] (* Jean-François Alcover, Dec 11 2014, after Vladeta Jovovic *)

CROSSREFS

A diagonal of A060044.

Sequence in context: A144252 A248033 A318254 * A089145 A324644 A134199

Adjacent sequences:  A002127 A002128 A002129 * A002131 A002132 A002133

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane.

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 November 30 08:19 EST 2021. Contains 349419 sequences. (Running on oeis4.)