A228948 Numbers n such that n^3 + k^2 = m^3 for some k>0, m>0.

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

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