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

1,1

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

Links

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

Example

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

Mathematica

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

Crossrefs

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

Cf. A000537, A265845.

Sequence in context: A232835 A223272 A265845 * A269139 A231319 A269197

Adjacent sequences: A131640 A131641 A131642 * A131644 A131645 A131646

Keyword

nonn

Author

Tanya Khovanova, Sep 08 2007

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

Status

approved