A131574 Numbers n that are the product of two distinct odd primes and x^2 + y^2 = n has integer solutions.

65, 85, 145, 185, 205, 221, 265, 305, 365, 377, 445, 481, 485, 493, 505, 533, 545, 565, 629, 685, 689, 697, 745, 785, 793, 865, 901, 905, 949, 965, 985, 1037, 1073, 1145, 1157, 1165, 1189, 1205, 1241, 1261, 1285, 1313, 1345, 1385, 1405, 1417, 1465, 1469

Offset: 1

Author

Colin Barker, Aug 28 2007, corrected Aug 29 2007

Keywords

• nonn

Comments

The two primes are of the form 4*k + 1.

Examples

			65 is in the sequence because x^2 + y^2 = 65 = 5*13 has solutions (x,y) = (1,8), (4,7), (7,4) and (8,1).
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Colin Barker)

Crossrefs

Cf. A000415, A121387, A248649, A248712, A264498, A264499

Programs

PARI

dop(d, nmax) = {
  my(L=List(), v=vector(d,m,1)~, f);
  for(n=1, nmax,
    f=factorint(n);
    if(#f~==d && f[1,1]>2 && f[,2]==v && f[,1]%4==v, listput(L, n))
  );
  Vec(L)
}
dop(2, 3000) \\ Colin Barker, Nov 15 2015