%I #24 Aug 04 2024 20:48:41
%S 3,1,2,1331,4,216,28,54872,116,343,828,250047,496,71991296,207
%N a(n) = least positive k such that Mordell's equation y^2 = x^3 - k has exactly n integral solutions.
%C The status of further terms is:
%C 15 integral solutions: unknown
%C 16 integral solutions: 503
%C 17 integral solutions: unknown
%C 18 integral solutions: 431
%C 19 integral solutions: unknown
%C 20 integral solutions: 2351
%C 21 integral solutions: unknown
%C 22 integral solutions: 3807
%C For least positive k such that equation y^2 = x^3 + k has exactly n integral solutions, see A179162.
%C If n is odd, then a(n) is perfect cube. [Ray Chandler]
%C From _Jose Aranda_, Aug 04 2024: (Start)
%C About those unknown terms:
%C a(15) <= 2600^3 = (26* 10^2)^3
%C a(17) <= 10400^3 = (26* 20^2)^3
%C a(19) <= 93600^3 = (26* 60^2)^3
%C a(21) <= 4586400^3 = (26*420^2)^3
%C The term a(13) = 71991296 = 416^3 = (26*4^2)^3. (End)
%H J. Gebel, <a href="/A001014/a001014.txt">Integer points on Mordell curves</a> [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
%Y Cf. A081120, A081121, A179163-A179174.
%K nonn,hard,more
%O 0,1
%A _Artur Jasinski_, Jun 30 2010
%E Edited and a(7), a(11), a(13) added by _Ray Chandler_, Jul 11 2010