A077115 Least integer square >= n^3.

0, 1, 9, 36, 64, 144, 225, 361, 529, 729, 1024, 1369, 1764, 2209, 2809, 3481, 4096, 5041, 5929, 6889, 8100, 9409, 10816, 12321, 13924, 15625, 17689, 19881, 22201, 24649, 27225, 29929, 33124, 36100, 39601, 43264, 46656, 51076, 55225, 59536

Offset: 0

Author

Reinhard Zumkeller, Oct 29 2002

Keywords

• nonn
• easy

Examples

			a(10) = 1024, as 1024 = 32^2 is the least square >= 1000 = 10^3.
		

Crossrefs

Cf. A000290, A000578, A048761, A065733, A077107, A077118, A185549.

Programs

Magma

[Ceiling(n^(3/2))^2: n in [0..50]]; // Vincenzo Librandi, Feb 17 2015

Mathematica

lis[n_]:=Module[{c=Sqrt[n^3]},If[IntegerQ[c],c^2,(Floor[c]+1)^2]]; Array[lis,40,0] (* Harvey P. Dale, Jan 22 2013 *)

Formula

a(n) - A070929(n) = n^3.

a(n) = ceiling(n^(3/2))^2. - Benoit Cloitre, Nov 01 2002

a(n) = A185549(n)^2. - Amiram Eldar, May 17 2025

a(n) = A048761(n^3). - Michel Marcus, May 17 2025