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A077113
Number of integer cubes <= n^2.
3
1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19
OFFSET
0,2
COMMENTS
a(n) is the least number m such that m^3 > n^2. - Zak Seidov, May 03 2005
FORMULA
a(n) = floor(n^(2/3))+1.
a(n) = [x^(n^2)] (1/(1 - x))*Sum_{k>=0} x^(k^3). - Ilya Gutkovskiy, Apr 20 2018
EXAMPLE
Cubes <= 10^2: 0, 1, 8, 27 and 64, hence a(10)=5;
MATHEMATICA
Table[Floor[n^(2/3) + 1], {n, 0, 100}] (* Zak Seidov, May 03 2005 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 29 2002
EXTENSIONS
Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar
STATUS
approved