A121536 Smallest m such that m^3 >= n^2.

0, 1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 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, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19

Offset: 1

Author

Zak Seidov, Aug 05 2006

Keywords

• nonn
• easy

Crossrefs

Cf. A070923, A077107, A100196.

Programs

Mathematica

Table[Ceiling[n^(2/3)],{n,1,100}]

Formula

a(n) = ceiling(n^(2/3)).

a(n) = (A070923(n)+n^2)^(1/3).

If n is a cube a(n) = A100196(n), otherwise a(n) = A100196(n)+1.

a(n) = A077107(n)^(1/3). - Amiram Eldar, May 17 2025

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, May 17 2025