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A309176
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a(n) = n^2 * (n + 1)/2 - Sum_{k=1..n} sigma_2(k).
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2
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0, 0, 2, 3, 12, 13, 33, 40, 66, 81, 135, 135, 212, 249, 319, 354, 489, 511, 681, 725, 876, 981, 1233, 1235, 1509, 1660, 1920, 2032, 2437, 2472, 2936, 3091, 3488, 3755, 4275, 4290, 4955, 5292, 5854, 6024, 6843, 6968, 7870, 8190, 8839, 9340, 10420, 10442, 11568, 12038, 13014, 13474, 14851, 15098, 16436
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OFFSET
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1,3
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
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FORMULA
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G.f.: x * (1 + 2*x)/(1 - x)^4 - (1/(1 - x)) * Sum_{k>=1} k^2 * x^k/(1 - x^k).
a(n) = Sum_{k=1..n} (n mod k) * k.
a(n) = A002411(n) - A064602(n).
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MATHEMATICA
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Table[n^2 (n + 1)/2 - Sum[DivisorSigma[2, k], {k, 1, n}], {n, 1, 55}]
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
Table[Sum[Mod[n, k] k, {k, 1, n}], {n, 1, 55}]
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PROG
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(PARI) a(n) = n^2*(n+1)/2 - sum(k=1, n, sigma(k, 2)); \\ Michel Marcus, Sep 18 2021
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CROSSREFS
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Cf. A000326, A001157, A004125, A048158, A051126, A154585, A256532.
Cf. A002411, A064602.
Sequence in context: A157902 A102660 A081347 * A074347 A102034 A102150
Adjacent sequences: A309173 A309174 A309175 * A309177 A309178 A309179
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Jul 15 2019
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STATUS
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approved
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