A033198 Discriminants of real quadratic number fields.

8, 12, 5, 24, 28, 40, 44, 13, 56, 60, 17, 76, 21, 88, 92, 104, 29, 120, 124, 33, 136, 140, 37, 152, 156, 41, 168, 172, 184, 188, 204, 53, 220, 57, 232, 236, 61, 248, 65, 264, 268, 69, 280, 284, 73, 296, 77, 312, 316, 328, 332, 85, 344, 348, 89, 364, 93, 376, 380, 97

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 103.

Crossrefs

Cf. A144338.

Programs

Maple

with(numtheory): a:= proc(n) if issqrfree(n) then RETURN(piecewise(n mod 4=1,n,4*n)) else RETURN(NULL) fi: end: seq(a(n),n=2..150); # C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 03 2005

Mathematica

Reap[For[n = 2, n <= 100, n++, If[SquareFreeQ[n], Sow[If[Mod[n, 4] == 1, n, 4 n]]]]][[2, 1]] (* Jean-François Alcover, Mar 22 2023 *)

Formula

For squarefree n >= 2, list n if n=1 mod 4 else 4n.

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 03 2005