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A103251 Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and z is a perfect square.

%I A103251 #20 Nov 14 2019 17:56:46
%S A103251 24,96,120,216,240,336,384,480,600,720,840,840,864,960,1080,1176,1320,
%T A103251 1344,1536,1920,1944,2016,2160,2184,2400,2520,2880,2904,3000,3024,
%U A103251 3360,3360,3360,3456,3696,3840,3960,4056,4320,4704,4896,5280,5280,5376,5400
%N A103251 Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and z is a perfect square.
%C A103251 There exists no case in which x or y and z are squares.
%C A103251 Also area A of the right triangles such that A, the sides and the circumradius are integers. - _Michel Lagneau_, Mar 15 2012
%H A103251 MathForFun, <a href="http://groups.yahoo.com/group/mathforfun/message/9962">Pythagorean triples</a>
%H A103251 Chenglong Zou, Peter Otzen, Cino Hilliard, <a href="/A103246/a103246.txt">Pythagorean triplets</a>, digest of 6 messages in mathfun Yahoo group, Mar 19, 2005.
%e A103251 x=24, y=7, 24^2 + 7^2 = 25^2. 24 is the 1st entry in the list.
%o A103251 (PARI) pythtrisq(n) = { local(a,b,c=0,k,x,y,z,vy,wx,vx,vz,j); w = vector(n*n+1); for(a=1,n, for(b=1,n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 & issquare(z), c++; w[c]=x; print(x","y","z) ) ) ); vx=vector(c); w=vecsort(w); for(j=1,n*n, if(w[j]>0, k++; vx[k]=w[j]; ) ); for(j=1,200, print1(vx[j]",") ) }
%K A103251 easy,nonn
%O A103251 1,1
%A A103251 _Cino Hilliard_, Mar 20 2005