A319088 a(n) = Sum_{k=1..n} k^2*tau_3(k), where tau_3 is A007425.

1, 13, 40, 136, 211, 535, 682, 1322, 1808, 2708, 3071, 5663, 6170, 7934, 9959, 13799, 14666, 20498, 21581, 28781, 32750, 37106, 38693, 55973, 59723, 65807, 73097, 87209, 89732, 114032, 116915, 138419, 148220, 158624, 169649, 216305, 220412, 233408, 247097

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Stieltjes Constants

Wikipedia, Stieltjes constants

Formula

a(n) ~ n^3 * (log(n)^2/6 + (gamma - 1/9)*log(n) + gamma^2 - gamma/3 - g1 + 1/27), where gamma is the Euler-Mascheroni constant A001620 and g1 is the first Stieltjes constant A082633.

Mathematica

nmax = 50; Accumulate[Table[k^2*Sum[DivisorSigma[0, d], {d, Divisors[k]}], {k, 1, nmax}]]

Crossrefs

Cf. A007425, A061201, A318750.

Sequence in context: A041324 A220083 A041326 * A041755 A229768 A251100

Adjacent sequences: A319085 A319086 A319087 * A319089 A319090 A319091

Keyword

nonn

Author

Vaclav Kotesovec, Sep 10 2018

Status

approved