%I #11 Apr 14 2015 10:30:31

%S 69,70,132,138,140,153,198,207,210,216,238,252,264,264,264,270,276,

%T 280,285,290,306,345,350,390,396,396,414,420,429,432,459,476,483,490,

%U 504,504,520,528,528,528,539,540,552,560,567,570,580,594,595,612,621,630

%N The radius of the largest of four circles with different integer radii arranged so that each circle is tangent externally to the other three circles.

%H Kival Ngaokrajang, <a href="/A256694/a256694.pdf">Illustration of the first three solutions</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SoddyCircles.html">Soddy Circles.</a>

%o (PARI)

%o soddy(k) = {

%o s=[];

%o for(a=1, k,

%o for(b=1, a-1,

%o for(c=1, b-1,

%o if(issquare(a*b*c*(a+b+c), &t),

%o if(a*b*c % (a*b+a*c+b*c+2*t) == 0,

%o s=concat(s, a)

%o )

%o )

%o )

%o )

%o );

%o s

%o }

%o soddy(500)

%Y See also the many sequences arising from Apollonian circle packing: A135849, A137246, A154636, etc.

%Y Also the sequences related to Soddy's circle packings: A046159, A046160, A062536, etc.

%K nonn

%O 1,1

%A _Colin Barker_, Apr 08 2015