login
Largest cube <= n.
10

%I #24 Aug 15 2022 04:31:01

%S 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,

%T 27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,

%U 27,27,27,27,27,27,27,27,27,64,64,64

%N Largest cube <= n.

%D 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.

%D 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.

%H Reinhard Zumkeller, <a href="/A048762/b048762.txt">Table of n, a(n) for n = 0..10000</a>

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

%H Krassimir T. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">On Some of Smarandache's Problems</a>, American Research Press, 1999, 27-32.

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

%p A048762 := proc(n)

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

%p %^3 ;

%p end proc: # _R. J. Mathar_, Nov 06 2011

%t Floor[Surd[Range[0,70],3]]^3 (* _Harvey P. Dale_, Jun 23 2013 *)

%o (Haskell)

%o a048762 n = last $ takeWhile (<= n) a000578_list

%o -- _Reinhard Zumkeller_, Nov 28 2011

%Y Cf. A048763, A201053, A000578.

%K nonn

%O 0,9

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