

A228948


Numbers n such that n^3 + k^2 = m^3 for some k>0, m>0.


5



6, 7, 11, 23, 24, 26, 28, 31, 38, 42, 44, 47, 54, 55, 61, 63, 84, 91, 92, 95, 96, 99, 104, 110, 111, 112, 118, 119, 124, 138
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OFFSET

1,1


COMMENTS

Cube root of perfect cubes in A087285 or in A229618 are in the present sequence, but this does not yield all terms, because these sequences require k^2 to be the largest square < m^3.
Numbers k such that Mordell's equation y^2 = x^3  k^3 has more than 1 integral solution. (Note that it is necessary that x is positive.) In other words, numbers k such that Mordell's equation y^2 = x^3  k^3 has solutions other than the trivial solution (k,0).  Jianing Song, Sep 24 2022


LINKS



EXAMPLE

6 is a term since the equation y^2 = x^3  6^3 has 5 solutions (6,0), (10,+28), and (33,+189).  Jianing Song, Sep 24 2022


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



