cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A118014 #15 Sep 13 2024 00:39:33
%S A118014 0,1,6,16,33,56,88,125,172,227,291,363,445,533,633,743,861,989,1128,
%T A118014 1275,1434,1601,1779,1967,2170,2376,2597,2827,3072,3324,3588,3859,
%U A118014 4143,4439,4749,5070,5399,5738,6091,6458,6834,7221,7618,8027,8448,8884,9329,9783
%N A118014 a(n) = Sum_{k=1..n} floor(n^2/k).
%C A118014 Sums of rows of triangle in A118013.
%C A118014 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]
%F A118014 a(n) = Sum_{k=1..n} A118013(n,k).
%F A118014 a(n) ~ (gamma + log(n)) * n^2, where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Dec 22 2020
%p A118014 Digits:=200; f:=n->add(floor( n^2/k ),k=1..n );
%t A118014 Table[Total[Floor[n^2/Range[n]]],{n,0,60}] (* _Harvey P. Dale_, Jun 04 2023 *)
%Y A118014 Cf. A006218, A069627, A118013.
%K A118014 nonn
%O A118014 0,3
%A A118014 _Reinhard Zumkeller_, Apr 10 2006
%E A118014 Edited by _N. J. A. Sloane_, Oct 28 2008