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A002130 Generalized sum of divisors function.
(Formerly M2238 N0888)

%I M2238 N0888

%S 1,-1,1,3,-2,1,-5,23,-25,27,-49,74,-62,85,-132,165,-195,229,-240,325,

%T -374,379,-469,553,-590,746,-805,854,-1000,1085,-1168,1284,-1396,1668,

%U -1767,1815,-2030,2297,-2450,2480,-2849,3293,-3113,3278,-3772,4091,-4230,4213,-4830,5607,-5499,5430,-6018,6922,-6880

%N 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 P. A. MacMahon, <a href="https://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 (1919), 75-113; Coll. Papers II, pp. 303-341.

%F 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

%t 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-Fran├žois Alcover_, Dec 11 2014, after _Vladeta Jovovic_ *)

%Y A diagonal of A060044.

%K sign,easy

%O 3,4

%A _N. J. A. Sloane_.

%E More terms from _Naohiro Nomoto_, Jan 24 2002

%E More terms from _Vladeta Jovovic_, Sep 21 2007

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)