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%I #15 Nov 14 2019 17:55:29
%S 30,40,120,130,160,270,272,312,350,360,480,510,520,640,738,750,888,
%T 1000,1080,1088,1160,1170,1200,1218,1248,1342,1400,1440,1470,1920,
%U 1960,2040,2080,2080,2210,2430,2448,2560,2590,2808,2952,2968,3000,3150,3240,3250
%N Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and y is a perfect square.
%C The case where x and y are both squares cannot occur.
%H MathForFun, <a href="http://groups.yahoo.com/group/mathforfun/message/9962">Pythagorean triples</a>
%H 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 x=30, y=16, 30^2 + 16^2 = 34^2. 30 is the 1st entry in the list.
%o (PARI) pythtrisq(n) = { local(a,b,c=0,k,x,y,z,vy,wx,vx,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(y), 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 easy,nonn
%O 1,1
%A _Cino Hilliard_, Mar 19 2005
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