A228948 - OEIS

%I #24 Sep 24 2022 12:29:00

%S 6,7,11,23,24,26,28,31,38,42,44,47,54,55,61,63,84,91,92,95,96,99,104,

%T 110,111,112,118,119,124,138

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

%C 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.

%C 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

%e 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

%Y Cf. A229618, A087285, A087286, A088017, A081121, A081120, A077116, A065733.

%Y Cube root of A179419.

%Y Cf. A356709, A356720. Complement of A356713.

%K nonn

%O 1,1

%A _M. F. Hasler_, Oct 05 2013

%E More terms added by _Jianing Song_, Sep 24 2022 based on A179419.