A118014 a(n) = Sum_{k=1..n} floor(n^2/k).

0, 1, 6, 16, 33, 56, 88, 125, 172, 227, 291, 363, 445, 533, 633, 743, 861, 989, 1128, 1275, 1434, 1601, 1779, 1967, 2170, 2376, 2597, 2827, 3072, 3324, 3588, 3859, 4143, 4439, 4749, 5070, 5399, 5738, 6091, 6458, 6834, 7221, 7618, 8027, 8448, 8884, 9329, 9783

Offset: 0

Author

Reinhard Zumkeller, Apr 10 2006

Keywords

• nonn

Comments

Sums of rows of triangle in A118013.

Generalized sequence: a(n)= Sum_{k=1..n} floor((k*t + n^2)/k) = t*n + Sum_{k=1..n} floor(n^2/k) = t*A000027(n)+ A118014(n). This sequence has t=0. [From Ctibor O. Zizka, Feb 14 2009]

Crossrefs

Cf. A006218, A069627, A118013.

Programs

Maple

Digits:=200; f:=n->add(floor( n^2/k ),k=1..n );

Mathematica

Table[Total[Floor[n^2/Range[n]]],{n,0,60}] (* Harvey P. Dale, Jun 04 2023 *)

Formula

a(n) = Sum_{k=1..n} A118013(n,k).

a(n) ~ (gamma + log(n)) * n^2, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Dec 22 2020

Extensions

Edited by N. J. A. Sloane, Oct 28 2008