A191483 Even discriminants of imaginary quadratic fields, negated.

4, 8, 20, 24, 40, 52, 56, 68, 84, 88, 104, 116, 120, 132, 136, 148, 152, 164, 168, 184, 212, 228, 232, 244, 248, 260, 264, 276, 280, 292, 296, 308, 312, 328, 340, 344, 356, 372, 376, 388, 404, 408, 420, 424, 436, 440, 452, 456, 472, 488, 516, 520, 532, 536, 548

Offset: 1

Author

Robert G. Wilson v, Jun 04 2011

Keywords

• easy
• nonn

Comments

Terms of A003657 that are not in A039957.

The asymptotic density of this sequence is 1/Pi^2 (A092742). - Amiram Eldar, Feb 23 2021

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A003657, A039957, A089269, A092742.

Programs

Mathematica

FundamentalDiscriminantQ[n_Integer] := n != 1 && (Mod[n, 4] == 1 || ! Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via Eric E. Weisstein *); -Select[-Range@550, FundamentalDiscriminantQ@# && EvenQ@# &]
(* Second program: *)
Select[Range[600], Mod[#, 4] == 0 && SquareFreeQ[#/4] && Mod[#, 16] != 12&] (* Jean-François Alcover, Jul 25 2019, after Andrew Howroyd *)

PARI

ok(n)={isfundamental(-n) && n%2==0} \\ Andrew Howroyd, Jul 25 2018

PARI

ok(n)={n%4==0 && issquarefree(n/4) && n%16<>12} \\ Andrew Howroyd, Jul 25 2018

Formula

Complement(A003657, A039957).

a(n) = 4*A089269(n). - Andrew Howroyd, Jul 25 2018