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.

24, 96, 120, 216, 240, 336, 384, 480, 600, 720, 840, 840, 864, 960, 1080, 1176, 1320, 1344, 1536, 1920, 1944, 2016, 2160, 2184, 2400, 2520, 2880, 2904, 3000, 3024, 3360, 3360, 3360, 3456, 3696, 3840, 3960, 4056, 4320, 4704, 4896, 5280, 5280, 5376, 5400

Offset: 1

Author

Cino Hilliard, Mar 20 2005

Keywords

• easy
• nonn

Comments

There exists no case in which x or y and z are squares.

Also area A of the right triangles such that A, the sides and the circumradius are integers. - Michel Lagneau, Mar 15 2012

Examples

			x=24, y=7, 24^2 + 7^2 = 25^2. 24 is the 1st entry in the list.
		

Links

• MathForFun, Pythagorean triples
• Chenglong Zou, Peter Otzen, Cino Hilliard, Pythagorean triplets, digest of 6 messages in mathfun Yahoo group, Mar 19, 2005.

Programs

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]",") ) }