A034715 Dirichlet convolution of triangular numbers with themselves.

1, 6, 12, 29, 30, 78, 56, 132, 126, 200, 132, 402, 182, 378, 420, 588, 306, 864, 380, 1050, 798, 902, 552, 1920, 875, 1248, 1296, 2002, 870, 2940, 992, 2592, 1914, 2108, 2100, 4635, 1406, 2622, 2652, 5080, 1722, 5628, 1892, 4818, 4860, 3818, 2256, 8856

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• changed

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217.

Programs

Magma

A000217:=func; [&+[A000217(d)*A000217(n div d): d in Divisors(n)]: n in [1..50]]; // Bruno Berselli, Feb 11 2014

Mathematica

Table[n/4*Sum[(n+d)*(d+1)/d, {d, Divisors[n]}], {n, 1, 50}] (* Vaclav Kotesovec, Feb 05 2019 *)

Formula

G.f.: Sum_{k>=1} (k*(k + 1)/2)*x^k/(1 - x^k)^3. - Ilya Gutkovskiy, Oct 24 2018

From Vaclav Kotesovec, Feb 05 2019: (Start)

Dirichlet g.f.: ((zeta(s-1) + zeta(s-2))/2)^2.

Sum_{k=1..n} a(k) ~ n^3*(log(n)/12 + (6*gamma - 1 + Pi^2)/36), where gamma is the Euler-Mascheroni constant A001620. (End)