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

0,17

Comments

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

Links

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

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

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)]

Prog

(PARI) vector(100, n, n--; floor(n^(1/4)))
(PARI) a(n) = sqrtnint(n, 4); \\ Michel Marcus, Dec 22 2016
(SageMath) [floor(n^(1/4)) for n in (0..100)]
(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
(Python)
from sympy import integer_nthroot
def A255270(n): return integer_nthroot(n, 4)[0] # Chai Wah Wu, Jun 06 2025

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.

Sequence in context: A138902 A211668 A390767 * A211670 A036452 A390766

Adjacent sequences: A255267 A255268 A255269 * A255271 A255272 A255273

Keyword

nonn,easy

Author

Bruno Berselli, Feb 20 2015

Status

approved