login
A178487
a(n) = floor(n^(1/5)): integer part of fifth root of n.
5
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
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).
Sequence in context: A113679 A262438 A044931 * A280560 A044932 A211669
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Oct 09 2010
STATUS
approved