%I #14 Nov 14 2019 17:59:25
%S 7,28,41,63,112,119,161,164,175,239,252,343,369,448,476,527,567,644,
%T 656,700,721,847,956,959,1008,1025,1071,1081,1183,1241,1372,1449,1476,
%U 1519,1575,1792,1904,2009,2023,2047,2108,2268,2527,2576,2624,2800,2884,2975
%N Numbers y, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and z is a perfect square.
%C The case where x or y and z are squares does not 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=24, y=7, 24^2 + 7^2 = 25^2. 7 is the 1st entry in the list.
%o (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]=y; print(x","y","z) ) ) ); vy=vector(c); w=vecsort(w); for(j=1,n*n, if(w[j]>0, k++; vy[k]=w[j]; ) ); for(j=1,200, print1(vy[j]",") ) }
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Mar 20 2005
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