A048763 Smallest cube >= n.

0, 1, 8, 8, 8, 8, 8, 8, 8, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 125, 125, 125, 125, 125, 125

Offset: 0

Author

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

Keywords

• nonn

References

• Krassimir T. Atanassov, On the 40th and 41st Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 4, No. 3 (1998), 101-104.
• J. Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3 (1999), 202-204.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Krassimir T. Atanassov, On Some of Smarandache's Problems, American Research Press, 1999, 27-32.
• Florentin Smarandache, Only Problems, Not Solutions!.

Crossrefs

Cf. A048762, A201053, A000578.

Programs

Haskell

a048763 0 = 0
a048763 n = head $ dropWhile (< n) a000578_list
-- Reinhard Zumkeller, Nov 28 2011

Maple

A048763 := proc(n)
        ceil(root[3](n)) ;
        %^3 ;
end proc: # R. J. Mathar, Nov 06 2011

Mathematica

With[{nn=80},Flatten[Table[Select[Range[0,Floor[nn^(1/3)]+1]^3,#>=n&,1],{n,0,nn}]]] (* Harvey P. Dale, Aug 09 2012 *)

Formula

Sum_{n>=1} 1/a(n)^2 = Pi^4/30 + Pi^6/945 - 3*zeta(5). - Amiram Eldar, Aug 15 2022

Extensions

a(65), a(66) and a(67) corrected by Reinhard Zumkeller, Nov 28 2011