A048762 Largest cube <= n.

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

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
• Florentin Smarandache, Only Problems, Not Solutions!.
• Krassimir T. Atanassov, On Some of Smarandache's Problems, American Research Press, 1999, 27-32.

Crossrefs

Cf. A048763, A201053, A000578.

Programs

Haskell

a048762 n = last $ takeWhile (<= n) a000578_list
-- Reinhard Zumkeller, Nov 28 2011

Maple

A048762 := proc(n)
        floor(root[3](n)) ;
        %^3 ;
end proc: # R. J. Mathar, Nov 06 2011

Mathematica

Floor[Surd[Range[0,70],3]]^3 (* Harvey P. Dale, Jun 23 2013 *)

Formula

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