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A344675
a(n) = Sum_{k=1..n} floor(n^3/k^3).
5
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
1,2
COMMENTS
In general, for m > 1, Sum_{k=1..n} floor(n^m/k^m) ~ zeta(m)*n^m + zeta(1/m)*n.
FORMULA
a(n) ~ zeta(3)*n^3 + zeta(1/3)*n.
MATHEMATICA
Table[Sum[Floor[n^3/k^3], {k, 1, n}], {n, 1, 50}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 26 2021
STATUS
approved