A077110 Nearest integer cube to n^2.

0, 1, 1, 8, 8, 27, 27, 64, 64, 64, 125, 125, 125, 125, 216, 216, 216, 343, 343, 343, 343, 512, 512, 512, 512, 729, 729, 729, 729, 729, 1000, 1000, 1000, 1000, 1000, 1331, 1331, 1331, 1331, 1331, 1728, 1728, 1728, 1728, 1728, 2197, 2197, 2197

Offset: 0

Author

Reinhard Zumkeller, Oct 29 2002

Keywords

• nonn
• easy

Examples

			a(10) = 125, as 125 = 5^3 is the nearest cube to 100 = 10^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000578, A000290, A075847, A070923, A077106, A077107, A077111, A077118.

Cf. A002760 (Squares and cubes). - Zak Seidov, Oct 08 2015

Programs

Mathematica

nic[n_]:=Module[{n2=n^2,s3,c1,c2},s3=Surd[n2,3];c1=Floor[s3]^3;c2= Ceiling[ s3]^3;If[n2-c1Harvey P. Dale, Jul 05 2015 *)

Python

from sympy import integer_nthroot
def A077110(n):
    n2 = n**2
    a = integer_nthroot(n2,3)[0]
    a2, a3 = a**3, (a+1)**3
    return a3 if a3+a2-2*n2 < 0 else a2 # Chai Wah Wu, Sep 24 2021

Formula

a(n) = if A075847(n) < A070923(n) then A077106(n) else A077107(n).