A178487 a(n) = floor(n^(1/5)): integer part of fifth root of n.

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

Offset: 0

Author

M. F. Hasler, Oct 09 2010

Keywords

• nonn
• easy

Comments

Each term k appears (k+1)^5 - k^5 times consecutively (A022521). - Bernard Schott, Mar 07 2023

Crossrefs

Sequences a(n) = floor(n^(1/k)): A001477 (k=1), A000196 (k=2), A048766 (k=3), A255270 (k=4), this sequence (k= 5), A178489 (k=6), A057427 (k->oo).

Cf. A022521, A253206.

Programs

Magma

[n eq 0 select 0 else Iroot(n, 5): n in [0..110]]; // Bruno Berselli, Feb 20 2015

Maple

seq(floor(n^(1/5)), n=0..100); # Ridouane Oudra, Feb 26 2023

Mathematica

Floor[Range[0,120]^(1/5)] (* Harvey P. Dale, Aug 15 2012 *)

PARI

A178487(n)=floor(sqrtn(n+.5,5))

PARI

a(n) = sqrtnint(n, 5); \\ Michel Marcus, Dec 22 2016

Python

from sympy import integer_nthroot
def A178487(n): return integer_nthroot(n,5)[0] # Chai Wah Wu, Jun 06 2025

Formula

G.f.: Sum_{k>=1} x^(k^5)/(1 - x). - Ilya Gutkovskiy, Dec 22 2016

a(n) = Sum_{i=1..n} A253206(i)*floor(n/i). - Ridouane Oudra, Feb 26 2023