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

Author

M. F. Hasler, Oct 05 2013

Keywords

• nonn

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

Examples

			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.

Extensions

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