

A131643


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


6



216, 8000, 64000, 216000, 343000, 5832000, 35937000, 157464000, 1540798875, 3951805941, 22069810125, 23295638016, 58230605376, 170400029184, 4767078987000, 19814511816000, 241152896222784, 565199024832000, 731189187729000, 5399901725184000, 13389040129314816, 15517248640897024
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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(i1) 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



