A344675 a(n) = Sum_{k=1..n} floor(n^3/k^3).

1, 9, 31, 75, 146, 256, 406, 610, 870, 1194, 1590, 2069, 2631, 3286, 4043, 4910, 5889, 6997, 8228, 9600, 11114, 12781, 14605, 16599, 18760, 21106, 23636, 26363, 29292, 32429, 35781, 39359, 43169, 47212, 51505, 56054, 60855, 65924, 71268, 76898, 82807, 89021

Offset: 1

Author

Vaclav Kotesovec, May 26 2021

Keywords

• nonn

Comments

In general, for m > 1, Sum_{k=1..n} floor(n^m/k^m) ~ zeta(m)*n^m + zeta(1/m)*n.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Plot of (a(n) - zeta(3)*n^3)/n for n = 1..100000

Crossrefs

Cf. A001158, A006218, A153818.

Programs

Mathematica

Table[Sum[Floor[n^3/k^3], {k, 1, n}], {n, 1, 50}]

Formula

a(n) ~ zeta(3)*n^3 + zeta(1/3)*n.