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
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!.
Programs
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Haskell
a048766 = round . (** (1/3)) . fromIntegral a048766_list = concatMap (\x -> take (a003215 x) $ repeat x) [0..] -- Reinhard Zumkeller, Sep 15 2013, Oct 22 2011
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Magma
[n eq 0 select 0 else Iroot(n,3): n in [0..110]]; // Bruno Berselli, Feb 20 2015
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Maple
A048766 := proc(n) floor(root[3](n)) ; end proc: seq(A048766(n),n=0..80) ; # R. J. Mathar, Dec 20 2020
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Mathematica
a[n_]:=IntegerPart[n^(1/3)];lst={};Do[AppendTo[lst, a[n]], {n, 0, 6!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 02 2008 *) -
PARI
a(n)=floor(n^(1/3)) \\ Charles R Greathouse IV, Mar 20 2012
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PARI
a(n) = sqrtnint(n, 3); \\ Michel Marcus, Nov 10 2015
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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
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
Extensions
Additional comments from Reinhard Zumkeller, Oct 07 2001
More terms from Benoit Cloitre, Jan 30 2003