A264499 Numbers n that are the product of four distinct odd primes and x^2 + y^2 = n has integer solutions.

32045, 40885, 45305, 58565, 67405, 69745, 77285, 80665, 91205, 98345, 98605, 99905, 101065, 107185, 111605, 114985, 120445, 124865, 127465, 128945, 130645, 137605, 141245, 146705, 150365, 151385, 162565, 164645, 166685, 167765, 173485, 175565, 179945, 182845

Offset: 1

Author

Colin Barker, Nov 15 2015

Keywords

• nonn

Comments

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

Examples

			32045 is in the sequence because x^2 + y^2 = 32045 = 5*13*17*29 has solutions (x,y) = (2,179), (19,178), (46,173), (67,166), (74,163), (86,157), (109,142) and (122,131).
		

Links

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

Crossrefs

Cf. A131574, A264498.

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(4, 200000)