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

0,33

Comments

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

Links

Table of n, a(n) for n=0..104.

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

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 *)

Prog

(PARI) A178487(n)=floor(sqrtn(n+.5, 5))
(PARI) a(n) = sqrtnint(n, 5); \\ Michel Marcus, Dec 22 2016
(Magma) [n eq 0 select 0 else Iroot(n, 5): n in [0..110]]; // Bruno Berselli, Feb 20 2015

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.

Sequence in context: A113679 A262438 A044931 * A280560 A044932 A211669

Adjacent sequences: A178484 A178485 A178486 * A178488 A178489 A178490

Keyword

nonn,easy

Author

M. F. Hasler, Oct 09 2010

Status

approved