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

1,2

Links

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

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)

Mathematica

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

Prog

(Magma) A000217:=func<i | i*(i+1)/2>; [&+[A000217(d)*A000217(n div d): d in Divisors(n)]: n in [1..50]]; // Bruno Berselli, Feb 11 2014

Crossrefs

Cf. A000217.

Sequence in context: A323652 A223346 A109510 * A294730 A079390 A124679

Adjacent sequences: A034712 A034713 A034714 * A034716 A034717 A034718

Keyword

nonn

Author

Erich Friedman

Status

approved