A077118 Nearest integer square to n^3.

0, 1, 9, 25, 64, 121, 225, 361, 529, 729, 1024, 1296, 1764, 2209, 2704, 3364, 4096, 4900, 5776, 6889, 7921, 9216, 10609, 12100, 13924, 15625, 17689, 19600, 21904, 24336, 26896, 29929, 32761, 36100, 39204, 42849, 46656, 50625, 54756, 59536

Offset

0,3

Links

Table of n, a(n) for n=0..39.

Formula

a(n) = if A077116(n) < A070929(n) then A065733(n) else A077115(n).

a(n) = A002821(n)^2. - Chai Wah Wu, Jul 30 2022

Example

a(5)=121, as 121=11^2 is the nearest square to 125=5^3.

Mathematica

Table[Round[Sqrt[n^3]]^2, {n, 0, 39}] (* Alonso del Arte, Dec 07 2011, based on Artur Jasinski's program for A077119 *)

Prog

(Python)
from math import isqrt
def A077118(n): return ((m:=isqrt(k:=n**3))+int((k-m*(m+1)<<2)>=1))**2 # Chai Wah Wu, Jul 29 2022

Crossrefs

Cf. A000290, A000578, A002821, A077119, A077110.

Sequence in context: A049740 A147405 A111440 * A242116 A209530 A147392

Adjacent sequences: A077115 A077116 A077117 * A077119 A077120 A077121

Keyword

nonn

Author

Reinhard Zumkeller, Oct 29 2002

Status

approved