

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

Table of n, a(n) for n=1..30.


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

Cf. A229618, A087285, A087286, A088017, A081121, A081120, A077116, A065733.
Cube root of A179419.
Cf. A356709, A356720. Complement of A356713.
Sequence in context: A297254 A347512 A296695 * A297128 A035110 A011990
Adjacent sequences: A228945 A228946 A228947 * A228949 A228950 A228951


KEYWORD

nonn


AUTHOR

M. F. Hasler, Oct 05 2013


EXTENSIONS

More terms added by Jianing Song, Sep 24 2022 based on A179419.


STATUS

approved



