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A327796 Values of x in the n solutions corresponding to the least number A300419(n) expressible in exactly n ways as x^2 + x*y + y^2 with x >= y >= 1, with x written as triangle T(n,k), k <= n. y is given in A327797.

%I A327796 #14 Jul 31 2021 22:55:19
%S A327796 1,6,9,17,21,23,25,32,37,40,91,107,118,143,154,66,77,89,94,98,109,392,
%T A327796 455,507,513,552,560,595,145,163,173,177,197,207,218,230,233,255,273,
%U A327796 310,325,335,357,378,390,462,498,539,561,623,658,686,711,717,763
%N A327796 Values of x in the n solutions corresponding to the least number A300419(n) expressible in exactly n ways as x^2 + x*y + y^2 with x >= y >= 1, with x written as triangle T(n,k), k <= n. y is given in A327797.
%C A327796 A combined table for the solutions corresponding to A300419(n) was provided by _Robert G. Wilson v_ as a text file, see link.
%H A327796 Hugo Pfoertner, <a href="/A327796/b327796.txt">Table of n, a(n) for n = 1..171</a>, rows 1..18 of triangle, flattened
%H A327796 Robert G. Wilson v, <a href="/A300419/a300419.txt">Solutions of a(n) for n <= 16</a>
%e A327796 The triangle begins
%e A327796     1,
%e A327796     6,   9,
%e A327796    17,  21,  23,
%e A327796    25,  32,  37,  40,
%e A327796    91, 107, 118, 143, 154,
%e A327796    66,  77,  89,  94,  98, 109,
%e A327796   392, 455, 507, 513, 552, 560, 595,
%e A327796   145, 163, 173, 177, 197, 207, 218, 230
%e A327796 .
%e A327796 T(3,1)=17, T(3,2)=21, T(3,3)=23 because
%e A327796 A300419(3) = 637 corresponds to the 3 solutions
%e A327796 637 = 17^2 + 17*12 + 12^2 = 21^2 + 21*7 + 7^2 = 23^2 + 23*4 + 4^2, using the y-values 12, 7, 4 from A327797.
%Y A327796 Cf. A300419, A327797.
%K A327796 nonn,tabl
%O A327796 1,2
%A A327796 _Hugo Pfoertner_, Sep 25 2019