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A280679 The radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.

%I A280679 #13 Feb 16 2025 08:33:39
%S A280679 36,9,4,144,16,9,225,100,36,400,25,16,784,441,144,900,36,25,1225,196,
%T A280679 100,1600,576,225,1764,49,36,2025,1296,400,3136,64,49,3969,324,196,
%U A280679 4356,3025,900,4900,900,441,5184,81,64,5929,1936,784,7056,3600,1225
%N A280679 The radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.
%H A280679 Colin Barker, <a href="/A280679/b280679.txt">Table of n, a(n) for n = 1..3000</a>
%H A280679 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TangentCircles.html">Tangent Circles</a>
%F A280679 The first few triples are [36, 9, 4], [144, 16, 9], [225, 100, 36], [400, 25, 16].
%o A280679 (PARI)
%o A280679 a280679(amax) = {
%o A280679   my(L=List());
%o A280679   for(a=1, amax,
%o A280679     for(b=1, a-1,
%o A280679       c=(1/(1/a + 1/b))^2;
%o A280679       if(type(c)=="t_INT" && gcd([a^2,b^2,c])==1,
%o A280679         listput(L, [a^2,b^2,c])
%o A280679       )
%o A280679     )
%o A280679   );
%o A280679   Vec(L)
%o A280679 }
%o A280679 concat(a280679(100))
%Y A280679 Cf. A265189, A280680.
%K A280679 nonn,tabf
%O A280679 1,1
%A A280679 _Colin Barker_, Jan 07 2017