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

1,1

Comments

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

Links

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

Example

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).

Prog

(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

Crossrefs

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

Sequence in context: A224770 A274044 A024409 * A323272 A322781 A020273

Adjacent sequences: A131571 A131572 A131573 * A131575 A131576 A131577

Keyword

nonn

Author

Colin Barker, Aug 28 2007, corrected Aug 29 2007

Status

approved