OFFSET
1,2
COMMENTS
Numbers k such that Mordell's equation y^2 = x^3 - k^3 has no solution other than the trivial solution (k,0).
Cube root of A179163.
Contains all squares: suppose that y^2 = x^3 - t^6, then (y/t^3)^2 = (x/t^2)^3 - 1. The elliptic curve Y^2 = X^3 - 1 has rank 0 and the only rational points on it are (1,0), so y^2 = x^3 - t^6 has only one solution (t^2,0).
LINKS
Jianing Song, Table of n, a(n) for n = 1..108 (using data from A179149)
FORMULA
1 is a term since the equation y^2 = x^3 - 1^3 has no solution other than (1,0).
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 23 2022
STATUS
approved