A024921 a(n) = Sum_{k=1..n} floor((n/k)*floor(n/k)).

1, 5, 11, 22, 33, 52, 67, 93, 117, 149, 174, 219, 250, 293, 339, 392, 434, 500, 546, 619, 680, 748, 804, 903, 969, 1051, 1131, 1230, 1301, 1422, 1497, 1609, 1708, 1814, 1915, 2062, 2156, 2275, 2388, 2543, 2646, 2808, 2915, 3070, 3219, 3359, 3480, 3683, 3813, 3985, 4137

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = n^2*Pi^2/6 + O(n*log n) as n -> infinity. - Robert Israel, Aug 05 2016

Maple

f:= n -> add(floor(n/k*floor(n/k)), k=1..n):
map(f, [$1..1000]); # Robert Israel, Aug 05 2016

Mathematica

Table[Sum[Floor[(n / k) Floor[n / k]], {k, 1, n}], {n, 1, 50}] (* Vincenzo Librandi, Jul 28 2019 *)

Prog

(PARI) a(n) = sum(k=1, n, floor((n/k)*floor(n/k)))  \\ Michel Marcus, Mar 23 2013
(Magma) [&+[(n div k)*(n div k): k in [1..n]]: n in [1..60]]; // Vincenzo Librandi, Jul 28 2019

Crossrefs

Sequence in context: A184552 A069097 A222548 * A189978 A192761 A152533

Adjacent sequences: A024918 A024919 A024920 * A024922 A024923 A024924

Keyword

nonn

Author

Clark Kimberling

Status

approved