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%I #12 Jan 10 2017 07:48:51
%S 36,9,4,144,16,9,225,100,36,400,25,16,784,441,144,900,36,25,1225,196,
%T 100,1600,576,225,1764,49,36,2025,1296,400,3136,64,49,3969,324,196,
%U 4356,3025,900,4900,900,441,5184,81,64,5929,1936,784,7056,3600,1225
%N The radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.
%H Colin Barker, <a href="/A280679/b280679.txt">Table of n, a(n) for n = 1..3000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TangentCircles.html">Tangent Circles</a>
%F The first few triples are [36, 9, 4], [144, 16, 9], [225, 100, 36], [400, 25, 16].
%o (PARI)
%o a280679(amax) = {
%o my(L=List());
%o for(a=1, amax,
%o for(b=1, a-1,
%o c=(1/(1/a + 1/b))^2;
%o if(type(c)=="t_INT" && gcd([a^2,b^2,c])==1,
%o listput(L, [a^2,b^2,c])
%o )
%o )
%o );
%o Vec(L)
%o }
%o concat(a280679(100))
%Y Cf. A265189, A280680.
%K nonn,tabf
%O 1,1
%A _Colin Barker_, Jan 07 2017
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