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

1,1

Comments

The four 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

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).

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(4, 200000)

Crossrefs

Cf. A131574, A264498.

Sequence in context: A217368 A359343 A097282 * A249230 A250897 A366512

Adjacent sequences: A264496 A264497 A264498 * A264500 A264501 A264502

Keyword

nonn

Author

Colin Barker, Nov 15 2015

Status

approved