A204993 Negative of the discriminant of quadratic field Q(sqrt(-n)).

4, 8, 3, 4, 20, 24, 7, 8, 4, 40, 11, 3, 52, 56, 15, 4, 68, 8, 19, 20, 84, 88, 23, 24, 4, 104, 3, 7, 116, 120, 31, 8, 132, 136, 35, 4, 148, 152, 39, 40, 164, 168, 43, 11, 20, 184, 47, 3, 4, 8, 51, 52, 212, 24, 55, 56, 228, 232, 59, 15, 244, 248, 7, 4, 260

Offset: 1

Author

Artur Jasinski, Jan 27 2012

Keywords

• nonn
• easy

Comments

For the discriminant of the quadratic field Q(sqrt(n)), see A037449.

a(n) is the smallest positive N such that ((-n)/k) = ((-n)/(k mod N)) for every odd k that is coprime to n, where ((-n)/k) is the Jacobi symbol. As we have Dirichlet's theorem on arithmetic progressions, a(n) is also the smallest positive N such that ((-n)/p) = ((-n)/(p mod N)) for every odd prime p that is not a factor of n. - Jianing Song, May 16 2024

Crossrefs

Cf. A037449, A007913.

Programs

Mathematica

-Table[NumberFieldDiscriminant[Sqrt[-n]], {n, 1, 70}]

PARI

a(n) = -quaddisc(-n) \\ Jianing Song, May 16 2024

Formula

Let b(n) = A007913(n), then a(n) = b(n) if b(n) == 3 (mod 4) and 4*b(n) otherwise. - Jianing Song, May 16 2024