login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%I #17 Sep 08 2022 08:46:24

%S 0,1,2,6,7,16,17,28,34,47,48,75,76,93,108,134,135,172,173,212,231,256,

%T 257,322,332,361,384,435,436,513,514,571,598,635,658,760,761,802,833,

%U 926,927,1028,1029,1104,1165,1214,1215,1358,1372,1453,1492,1579,1580,1705,1736,1857,1900,1961,1962

%N a(n) = Sum_{m=2..n} floor(n/m)^2.

%H Robert Israel, <a href="/A330476/b330476.txt">Table of n, a(n) for n = 1..5000</a>

%e a(4) = floor(4/2)^2 + floor(4/3)^2 + floor(4/4)^2 = 6.

%p f:= proc(n) local m; add(floor(n/m)^2,m=2..n) end proc:

%p map(f, [$1..100]);

%t Table[Sum[IntegerPart[(n/m)]^2,{m,2,n}],{n,1,100}] (* _Metin Sariyar_, Dec 15 2019 *)

%o (Magma) [0] cat [&+[Floor(n/m)^2:m in [2..n]]:n in [2..60]]; // _Marius A. Burtea_, Dec 15 2019

%Y Cf. A002541, A224526.

%K nonn

%O 1,3

%A _Robert Israel_, Dec 15 2019