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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 (list; graph; refs; listen; history; text; internal format)
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
Cube root of A179419.
Cf. A356709, A356720. Complement of A356713.
Sequence in context: A297254 A347512 A296695 * A297128 A035110 A011990
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 05 2013
EXTENSIONS
More terms added by Jianing Song, Sep 24 2022 based on A179419.
STATUS
approved

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Last modified June 13 08:31 EDT 2024. Contains 373383 sequences. (Running on oeis4.)