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A328259 a(n) = n * sigma_2(n). 0
1, 10, 30, 84, 130, 300, 350, 680, 819, 1300, 1342, 2520, 2210, 3500, 3900, 5456, 4930, 8190, 6878, 10920, 10500, 13420, 12190, 20400, 16275, 22100, 22140, 29400, 24418, 39000, 29822, 43680, 40260, 49300, 45500, 68796, 50690, 68780, 66300, 88400, 68962, 105000, 79550, 112728, 106470 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Moebius transform of A027847.

LINKS

Table of n, a(n) for n=1..45.

FORMULA

G.f.: Sum_{k>=1} k^3 * x^k / (1 - x^k)^2.

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

Dirichlet g.f.: zeta(s - 1) * zeta(s - 3).

Sum_{k=1..n} a(k) ~ zeta(3) * n^4 / 4. - Vaclav Kotesovec, Oct 09 2019

MATHEMATICA

Table[n DivisorSigma[2, n], {n, 1, 45}]

nmax = 45; CoefficientList[Series[Sum[k^3 x^k/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

CROSSREFS

Cf. A001157, A027847, A038040, A064987, A275585, A294362.

Sequence in context: A034127 A229466 A269261 * A005052 A057344 A115134

Adjacent sequences:  A328256 A328257 A328258 * A328260 A328261 A328262

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Oct 09 2019

STATUS

approved

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)