A131643 Cubes that are also sums of three or more consecutive positive cubes.

216, 8000, 64000, 216000, 343000, 5832000, 35937000, 157464000, 1540798875, 3951805941, 22069810125, 23295638016, 58230605376, 170400029184, 4767078987000, 19814511816000, 241152896222784, 565199024832000, 731189187729000, 5399901725184000, 13389040129314816, 15517248640897024

Offset: 1

Author

Tanya Khovanova, Sep 08 2007

Keywords

• nonn

Comments

Note that by Fermat's theorem no cube is the sum of two positive cubes.

All entries have the form A000537(j) - A000537(i-1) with 1 <= i < j, for example (j,i) = (5,3), (14,11), (22,3), (30,6), (34,15), (69,6), (109,11). - R. J. Mathar, Sep 14 2007 [Presumably this comment refers just to the terms shown, and not to every term in the sequence. - N. J. A. Sloane, Dec 19 2015]

Subsequence of A265845 (numbers that are sums of consecutive positive cubes in more than one way) which is sparse: among the first 1000 terms of A265845, only 17 are cubes. - Jonathan Sondow, Jan 10 2016

Examples

			216 = 27 + 64 + 125.
Note that "positive" is needed in the definition, otherwise the sequence would contain 8 = (-1)^3 + 0^3 + 1^3 + 2^3. - _N. J. A. Sloane_, Dec 19 2015
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..55 (terms < 2*10^23)

Crossrefs

a(n) = A097811(n)^3. - Donovan Johnson, Nov 09 2012

Cf. A000537, A265845.

Programs

Mathematica

Select[Union[ Flatten[Table[ Plus @@ Table[i^3, {i, k, j}], {k, 1000}, {j, k + 1, 1000}]]], # <= 1000^3 && IntegerQ[ #^(1/3)] &]

Extensions

More terms from R. J. Mathar, Sep 14 2007

More terms from Donovan Johnson, Mar 09 2008

Name edited by Jon E. Schoenfield, Dec 07 2015