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%I #9 Aug 24 2022 09:03:41
%S 3,7,1,2,8,329,217,506,65,260,585
%N a(n) is the least k such that Mordell's equation y^2 = x^3 + k^3 has exactly 2*n+1 integral solutions.
%C a(n) is the least k such that y^2 = x^3 + k^3 has exactly n solutions with y positive, or exactly n+1 solutions with y nonnegative.
%C a(n) is the smallest index of 2*n+1 in A356706, of n in A356707, and of n+1 in A356708.
%F a(n) = A179162(2*n+1)^(1/3).
%e a(4) = 8 since y^2 = x^3 + 8^3 has exactly 9 solutions (-8,0), (-7,+-13), (4,+-24), (8,+-32), and (184,+-2496), and the number of solutions to y^2 = x^3 + k^3 is not 9 for 0 < k < 8.
%Y Cf. A081119, A081120, A179162, A179175, A356705, A356706, A356707, A356708.
%K nonn,hard,more
%O 0,1
%A _Jianing Song_, Aug 23 2022