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A280680 The square roots of the radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.

%I A280680 #13 Feb 16 2025 08:33:39
%S A280680 6,3,2,12,4,3,15,10,6,20,5,4,28,21,12,30,6,5,35,14,10,40,24,15,42,7,6,
%T A280680 45,36,20,56,8,7,63,18,14,66,55,30,70,30,21,72,9,8,77,44,28,84,60,35,
%U A280680 88,33,24,90,10,9,91,78,42,99,22,18,104,65,40
%N A280680 The square roots of the radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.
%H A280680 Colin Barker, <a href="/A280680/b280680.txt">Table of n, a(n) for n = 1..3000</a>
%H A280680 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TangentCircles.html">Tangent Circles</a>
%e A280680 The first few triples are [6, 3, 2], [12, 4, 3], [15, 10, 6], [20, 5, 4].
%o A280680 (PARI)
%o A280680 a280680(amax) = {
%o A280680   my(L=List());
%o A280680   for(a=1, amax,
%o A280680     for(b=1, a-1,
%o A280680       c=(1/(1/a + 1/b))^2;
%o A280680       if(type(c)=="t_INT" && gcd([a^2,b^2,c])==1,
%o A280680         listput(L, [a,b,sqrtint(c)])
%o A280680       )
%o A280680     )
%o A280680   );
%o A280680   Vec(L)
%o A280680 }
%o A280680 concat(a280680(100))
%Y A280680 Cf. A106430, A246429, A247372, A265189, A280679.
%K A280680 nonn,tabf
%O A280680 1,1
%A A280680 _Colin Barker_, Jan 07 2017