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A356720 Numbers k such that Mordell's equation y^2 = x^3 + k^3 has more than 1 integral solution.

%I A356720 #18 Sep 24 2022 12:34:25
%S A356720 1,2,4,7,8,9,10,11,14,16,18,21,22,23,25,26,28,32,33,34,35,36,37,38,40,
%T A356720 44,46,49,50,56,57,63,64,65,70,71,72,74,78,81,84,86,88,90,91,92,95,98,
%U A356720 99,100,104,105,110,112,114,121,122,126,128,129,130,132,136,140,144,148
%N A356720 Numbers k such that Mordell's equation y^2 = x^3 + k^3 has more than 1 integral solution.
%C A356720 Numbers k such that Mordell's equation y^2 = x^3 + k^3 has solutions other than the trivial solution (-k,0).
%C A356720 Different from A103254, which lists k such that Mordell's equation y^2 = x^3 + k^3 has solutions with positive x (or equivalently, with nonnegative x). 71, 74, and 155 are here but not in A103254.
%C A356720 Cube root of A356703.
%C A356720 Contains all squares since A356711 does.
%H A356720 Jianing Song, <a href="/A356720/b356720.txt">Table of n, a(n) for n = 1..85</a> (based on the data from A103254)
%e A356720 71 is a term since the equation y^2 = x^3 + 71^3 has 3 solutions (-71,0) and (-23,+-588).
%e A356720 74 is a term since the equation y^2 = x^3 + 74^3 has 3 solutions (-74,0) and (-47,+-549).
%e A356720 155 is a term since the equation y^2 = x^3 + 155^3 has 3 solutions (-155,0) and (-31,+-1922).
%Y A356720 Cf. A081119, A356703, A356713, A228948, A103254. Complement of A356709.
%Y A356720 Cf. also A356710, A356711, A356712.
%K A356720 nonn
%O A356720 1,2
%A A356720 _Jianing Song_, Aug 24 2022