A048766 Integer part of cube root of n. Or, number of cubes <= n. Or, n appears 3n^2 + 3n + 1 times.

0, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

0,9

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

K. Atanassov, On the 100th, 101st and 102nd Smarandache Problems, On Some of Smarandache's Problems, American Research Press, 1999, pp. 57-61. Reprinted in Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 3, 94-96.

F. Smarandache, Only Problems, Not Solutions!.

Formula

G.f.: Sum_{k>=1} x^(k^3)/(1-x). - Geoffrey Critzer, Feb 05 2014

a(n) = Sum_{i=1..n} A210826(i)*floor(n/i). - Ridouane Oudra, Jan 21 2021

Maple

A048766 := proc(n)
    floor(root[3](n)) ;
end proc:
seq(A048766(n), n=0..80) ; # R. J. Mathar, Dec 20 2020

Mathematica

a[n_]:=IntegerPart[n^(1/3)]; lst={}; Do[AppendTo[lst, a[n]], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 02 2008 *)

Prog

(Haskell)
a048766 = round . (** (1/3)) . fromIntegral
a048766_list = concatMap (\x -> take (a003215 x) $ repeat x) [0..]
-- Reinhard Zumkeller, Sep 15 2013, Oct 22 2011
(PARI) a(n)=floor(n^(1/3)) \\ Charles R Greathouse IV, Mar 20 2012
(PARI) a(n) = sqrtnint(n, 3); \\ Michel Marcus, Nov 10 2015
(Magma) [n eq 0 select 0 else Iroot(n, 3): n in [0..110]]; // Bruno Berselli, Feb 20 2015
(Python)
from sympy import integer_nthroot
def a(n): return integer_nthroot(n, 3)[0]
print([a(n) for n in range(105)]) # Michael S. Branicky, Oct 19 2021

Crossrefs

Cf. A000196, A003215, A007412.

Sequence in context: A053230 A194334 A242259 * A105516 A105518 A111896

Adjacent sequences: A048763 A048764 A048765 * A048767 A048768 A048769

Keyword

nonn,easy

Author

Charles T. Le (charlestle(AT)yahoo.com)

Extensions

Additional comments from Reinhard Zumkeller, Oct 07 2001

More terms from Benoit Cloitre, Jan 30 2003

Status

approved