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

1,1

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

Links

Table of n, a(n) for n=1..45.

MathForFun, Pythagorean triples

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

Example

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

Prog

(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]", ") ) }

Crossrefs

Sequence in context: A090214 A283446 A208984 * A256418 A198387 A057102

Adjacent sequences: A103248 A103249 A103250 * A103252 A103253 A103254

Keyword

easy,nonn

Author

Cino Hilliard, Mar 20 2005

Status

approved