A024922 a(n) = Sum_{k=1..n} floor((n/k) * floor((n/k) * floor(n/k))).

1, 9, 29, 74, 140, 254, 391, 601, 851, 1183, 1546, 2058, 2580, 3244, 3986, 4876, 5795, 6959, 8105, 9540, 11012, 12692, 14391, 16546, 18590, 20966, 23425, 26255, 28992, 32344, 35472, 39173, 42886, 46974, 51075, 55963, 60475, 65602, 70781, 76696, 82244, 88826

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Formula

a(n) ~ zeta(3) * n^3. - Vaclav Kotesovec, May 28 2021

Mathematica

Total/@Table[Floor[n/k Floor[n/k Floor[n/k]]], {n, 50}, {k, n}] (* Harvey P. Dale, May 14 2013 *)
Table[Sum[Floor[n / k 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)*floor(n/k)))) \\ Michel Marcus, Mar 23 2013
(Magma) [&+[((n div k)*((n div k)*(n div k))): k in [1..n]]: n in [1..50]];  // Vincenzo Librandi, Jul 28 2019

Crossrefs

Sequence in context: A273268 A273306 A318742 * A193004 A198645 A045862

Adjacent sequences: A024919 A024920 A024921 * A024923 A024924 A024925

Keyword

nonn

Author

Clark Kimberling

Status

approved