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A106430 Ordered and uniqued length of side opposite the greater of the two angles, one being the double of the other, of a primitive integer-sided triangle.

%I A106430 #25 Sep 27 2014 19:09:50
%S A106430 6,12,15,20,28,30,35,40,42,45,56,63,66,70,72,77,84,88,90,91,99,104,
%T A106430 110,117,120,126,130,132,143,144,153,154,156,165,170,176,182,187,190,
%U A106430 195,198,204,208,209,210,220,221,228,231,234,238,240,247,255,260,266,272,273,276,285,286,299
%N A106430 Ordered and uniqued length of side opposite the greater of the two angles, one being the double of the other, of a primitive integer-sided triangle.
%C A106430 This is also the list of a, where a is positive integer solutions of 1/a+1/b=1/c and a>b>c and gcd[a,b,c]=1, sorted by ascending a, then b. See A247372 for list of b, A246429 for list of c. - _Albert Lau_, Sep 19 2014
%H A106430 Albert Lau, <a href="/A106430/b106430.txt">Table of n, a(n) for n = 1..10539</a>
%F A106430 Values r*s, where r<s<2r and (r, s)=1.
%F A106430 The other 2 sides are s^2 and r^2-s^2. - _Albert Lau_, Sep 19 2014
%t A106430 aMax = 300;
%t A106430 Select[Sequence @@@ Table[{m (m + n), n (m + n), m n}, {m, Sqrt[aMax]}, {n, Min[m - 1, aMax/m - m]}], GCD @@ # == 1 &] // Sort;
%t A106430 %[[;; , 1]]
%t A106430 (* _Albert Lau_, Sep 19 2014 *)
%Y A106430 Cf. A106499-A106506, A106410, A106420, A247372, A246429
%K A106430 nonn
%O A106430 1,1
%A A106430 _Lekraj Beedassy_ and _Ray Chandler_, May 09 2005