A055400 Cube excess: difference between n and largest cube <= n.

0, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

Offset: 0

Author

Henry Bottomley, May 16 2000

Keywords

• easy
• nonn

Examples

			a(12) = 4 because 2^3 <= 12 < 3^3 and 12 - 2^3 = 4.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A048762, A053186, A055401.

Programs

Maple

A055400 := proc(n)
        n-A048762(n) ;
end proc:
seq(A055400(n),n=0..80) ; # R. J. Mathar, Nov 06 2011

Mathematica

Array[#-Floor[Power[#, (3)^-1]]^3&,90,0] (* Harvey P. Dale, Jan 18 2012 *)

PARI

a(n)=n-sqrtnint(n,3)^3 \\ Charles R Greathouse IV, Sep 02 2015

Formula

a(n) = n - A048762(n) = n - floor(n^(1/3))^3.

a(n) < 3*n^(2/3) for n > 0. - Charles R Greathouse IV, Sep 02 2015