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A318750 a(n) = Sum_{k=1..n} k * tau_3(k), where tau_3 is A007425. 2
1, 7, 16, 40, 55, 109, 130, 210, 264, 354, 387, 603, 642, 768, 903, 1143, 1194, 1518, 1575, 1935, 2124, 2322, 2391, 3111, 3261, 3495, 3765, 4269, 4356, 5166, 5259, 5931, 6228, 6534, 6849, 8145, 8256, 8598, 8949, 10149, 10272, 11406, 11535, 12327, 13137, 13551 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..100000

Vaclav Kotesovec, Graph - The asymptotic ratio (1000000 terms)

FORMULA

a(n) = Sum_{k=1..n} A034718(k).

a(n) ~ n^2 * (log(n)^2 + (6*g-1)*log(n) + 6*g^2 - 3*g - 6*g1 + 1/2) / 4, where g is the Euler-Mascheroni constant A001620 and g1 is the first Stieltjes constant A082633. - Vaclav Kotesovec, Sep 09 2018

MATHEMATICA

Accumulate[Table[n*Sum[DivisorSigma[0, d], {d, Divisors[n]}], {n, 1, 100}]]

(* Asymptotics: *) n^2 * (Log[n]^2 + (6*EulerGamma - 1)*Log[n] + 6*EulerGamma^2 - 3*EulerGamma - 6*StieltjesGamma[1] + 1/2) / 4 (* Vaclav Kotesovec, Sep 09 2018 *)

CROSSREFS

Cf. A007425, A034718, A061201, A318413, A318414.

Sequence in context: A286710 A036834 A020941 * A024625 A055553 A066009

Adjacent sequences:  A318747 A318748 A318749 * A318751 A318752 A318753

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 02 2018

STATUS

approved

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Last modified June 4 07:23 EDT 2020. Contains 334822 sequences. (Running on oeis4.)