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A309176 a(n) = n^2 * (n + 1)/2 - Sum_{k=1..n} sigma_2(k). 1

%I

%S 0,0,2,3,12,13,33,40,66,81,135,135,212,249,319,354,489,511,681,725,

%T 876,981,1233,1235,1509,1660,1920,2032,2437,2472,2936,3091,3488,3755,

%U 4275,4290,4955,5292,5854,6024,6843,6968,7870,8190,8839,9340,10420,10442,11568,12038,13014,13474,14851,15098,16436

%N a(n) = n^2 * (n + 1)/2 - Sum_{k=1..n} sigma_2(k).

%F G.f.: x * (1 + 2*x)/(1 - x)^4 - (1/(1 - x)) * Sum_{k>=1} k^2 * x^k/(1 - x^k).

%F a(n) = Sum_{k=1..n} (n mod k) * k.

%F a(n) = A002411(n) - A064602(n).

%t Table[n^2 (n + 1)/2 - Sum[DivisorSigma[2, k], {k, 1, n}], {n, 1, 55}]

%t nmax = 55; CoefficientList[Series[x (1 + 2 x)/(1 - x)^4 - 1/(1 - x) Sum[k^2 x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%t Table[Sum[Mod[n, k] k, {k, 1, n}], {n, 1, 55}]

%Y Cf. A000326, A001157, A004125, A048158, A051126, A154585, A256532.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Jul 15 2019

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)