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%I #5 Nov 21 2019 08:15:47
%S 4,8,12,12,15,16,24,24,20,21,24,40,35,30,28,36,32,48,60,36,48,45,40,
%T 63,45,44,84,42,60,48,72,80,56,70,60,52,56,72,112,55,99,60,77,64,75,
%U 84,96,80,68,120,63,72,144,120,96,76,105,90,72,80,143,126,120,90,84,108,91
%N Middle side of a Pythagorean triangle (ordered by the product of the sides).
%F a(n) =A057096(n)/(A057098(n)*A057100(n)) =sqrt(A057100(n)^2-A057098(n)^2)
%e a(1)=4 since 3*4*5=60 is smallest possible positive product
%t maxShortLeg = 66; terms = 67;
%t r[a_] := {a, b, c} /. {ToRules[Reduce[a <= b < c && a^2+b^2 == c^2, {b, c}, Integers]]};
%t abc = r /@ Complement[Range[maxShortLeg], {1, 2, 4}] // Flatten[#, 1]&;
%t SortBy[abc, Times @@ # &][[;; terms, 2]] (* _Jean-François Alcover_, Nov 21 2019 *)
%Y Cf. A009012, A009023, A046084, A057096.
%K nonn
%O 1,1
%A _Henry Bottomley_, Aug 01 2000