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%I #6 Sep 02 2019 05:22:51
%S 129,2873,92218,101464,252092,322966,732516
%N Consider primitive solutions (x,y,z) to the system x+y+z = r^2, x^2+y^2+z^2 = s^2, x^3+y^3+z^3 = t^2, with 0<x<=y<=z arranged in order of increasing z; sequence gives z values.
%C A solution is primitive if it cannot be obtained multiplying another solution by a square greater than 1, i.e., if GCD(x,y,z) is squarefree.
%C The first two solutions are reported in Choudhry's paper, whose main purpose is providing a parametric solution.
%H Ajai Choudhry, <a href="https://arxiv.org/abs/1908.09742v1">A diophantine system</a>, arXiv:1908.09742v1 [math.NT], 2019.
%e 108 + 124 + 129 = 19^2, 108^2 + 124^2 + 129^2 = 209^2, 108^3 + 124^3 + 129^3 = 2305^2.
%Y The corresponding x and y values are in A327338 and A327339.
%Y Cf. A139266.
%K nonn,more
%O 1,1
%A _Giovanni Resta_, Sep 02 2019
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