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a(n) is the lesser coefficient of the pair (x, y) such that (x^2-y^2)/r, 2*x*y/r, (x^2+y^2)/r are the 2 legs and hypotenuse of the least Pythagorean triple having area A006991(n).
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%I #10 Jul 05 2023 15:03:56

%S 4,1,9,36,1,1,3,49,17689,4900,2,81,8,1764,289,12,16,49,2289169,

%T 1158313156,44,10227204,22801,4,169,2,121,2809,1,166952241,36,49,169,

%U 75,529,76,3975302500,1,7551929273974569,1764,1,12,19298449,25,305111826865145547009,143811,14161,3136,1,1

%N a(n) is the lesser coefficient of the pair (x, y) such that (x^2-y^2)/r, 2*x*y/r, (x^2+y^2)/r are the 2 legs and hypotenuse of the least Pythagorean triple having area A006991(n).

%H Michel Marcus, <a href="/A364109/b364109.txt">Table of n, a(n) for n = 1..361</a>

%H Mauro Fiorentini, <a href="http://bitman.name/math/table/29">Numeri congruenti minori di 1000</a>. See column b.

%H David Goldberg, <a href="https://arxiv.org/abs/2106.07373">Triangle Sides for Congruent Numbers less than 10,000</a>, arXiv:2106.07373 [math.NT], 2021. See column Q, p. 7.

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math10/matb2000.htm">Congruum</a>. See column n.

%Y Cf. A006991 (primitive congruent numbers), A364108 (x), A364110 (r).

%K nonn

%O 1,1

%A _Michel Marcus_, Jul 05 2023