A255270 Integer part of fourth root of n.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3

Offset: 0

Author

Bruno Berselli, Feb 20 2015

Keywords

• nonn
• easy

Comments

n appears (n+1)^4 - n^4 times (A005917).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A005917.

Cf. sequences of the type floor(n^(1/k)): A000196 (k=2), A048766 (k=3), this sequence (k=4), A178487 (k=5), A178489 (k=6).

Cf. A219009.

Programs

Magma

[IsZero(n) select 0 else Iroot(n, 4): n in [0..100]];

Magma

[Floor(n^(1/4)): n in [0..100]]; // Vincenzo Librandi, Feb 20 2015

Maple

A255270 := proc(n)
    floor( n^(1/4)) ;
end proc:
seq(A255270(n),n=0..100) ; # R. J. Mathar, May 08 2020

Mathematica

Floor[Range[0, 100]^(1/4)]

PARI

vector(100, n, n--; floor(n^(1/4)))

PARI

a(n) = sqrtnint(n, 4); \\ Michel Marcus, Dec 22 2016

Python

from sympy import integer_nthroot
def A255270(n): return integer_nthroot(n,4)[0] # Chai Wah Wu, Jun 06 2025

Sage

[floor(n^(1/4)) for n in (0..100)]

Formula

a(n) = floor(n^(1/4)) = floor(sqrt(A000196(n))).

G.f.: Sum_{k>=1} x^(k^4)/(1 - x). - Ilya Gutkovskiy, Dec 22 2016

a(n) = Sum_{i=1..n} A219009(i)*floor(n/i). - Ridouane Oudra, Feb 26 2023