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A103248 Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers.

%I A103248 #21 Nov 14 2019 17:48:59
%S A103248 16,24,36,44,56,60,64,68,76,84,88,92,96,100,104,116,120,124,128,132,
%T A103248 136,140,144,152,156,160,164,168,172,176,184,192,196,200,204,208,212,
%U A103248 216,220,224,228,236,240,244,252,256,264,272,276,280,284,288,296,300,304
%N A103248 Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers.
%H A103248 MathForFun, <a href="http://groups.yahoo.com/group/mathforfun/message/9962">Pythagorean triples</a>
%H A103248 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 A103248 x=16, y=63, 16^2 + 63^2 = 65^2. 16 is the 1st entry in the list.
%o A103248 (PARI) pythtri(n) = { local(a,b,c=0,k,x,y,z,vx,vy,wx,wyj); wx=wy= vector(n*n); 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 &!isprime(x) &!isprime(y) &!isprime(z), if(gcd(x,y)==1&gcd(x,z)==1&gcd(y,z)==1, c++; wy[c]=y; wx[c]=x; print(x","y","z); \ write("pythtri.txt",x","y","z); ) ) ) ); vy=vx=vector(c); wy=vecsort(wy); wx=vecsort(wx); for(j=1,n*n, if(wx[j]>0, k++; vx[k]=wx[j]; ); ); for(j=1,200, if(vx[j+1]<>vx[j],print1(vx[j]",")) ) }
%K A103248 easy,nonn
%O A103248 1,1
%A A103248 _Cino Hilliard_, Mar 19 2005