A048766 - OEIS

%I #61 Sep 08 2022 08:44:58

%S 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,

%T 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,

%U 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

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

%H Reinhard Zumkeller, <a href="/A048766/b048766.txt">Table of n, a(n) for n = 0..10000</a>

%H K. Atanassov, On the 100th, 101st and 102nd Smarandache Problems, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">On Some of Smarandache's Problems</a>, 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.

%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>.

%F G.f.: Sum_{k>=1} x^(k^3)/(1-x). - _Geoffrey Critzer_, Feb 05 2014

%F a(n) = Sum_{i=1..n} A210826(i)*floor(n/i). - _Ridouane Oudra_, Jan 21 2021

%p A048766 := proc(n)

%p     floor(root[3](n)) ;

%p end proc:

%p seq(A048766(n),n=0..80) ; # _R. J. Mathar_, Dec 20 2020

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

%o (Haskell)

%o a048766 = round . (** (1/3)) . fromIntegral

%o a048766_list = concatMap (\x -> take (a003215 x) $ repeat x) [0..]

%o -- _Reinhard Zumkeller_, Sep 15 2013, Oct 22 2011

%o (PARI) a(n)=floor(n^(1/3)) \\ _Charles R Greathouse IV_, Mar 20 2012

%o (PARI) a(n) = sqrtnint(n, 3); \\ _Michel Marcus_, Nov 10 2015

%o (Magma) [n eq 0 select 0 else Iroot(n,3): n in [0..110]]; // _Bruno Berselli_, Feb 20 2015

%o (Python)

%o from sympy import integer_nthroot

%o def a(n): return integer_nthroot(n, 3)[0]

%o print([a(n) for n in range(105)]) # _Michael S. Branicky_, Oct 19 2021

%Y Cf. A000196, A003215, A007412.

%K nonn,easy

%O 0,9

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

%E Additional comments from _Reinhard Zumkeller_, Oct 07 2001

%E More terms from _Benoit Cloitre_, Jan 30 2003