A072903 Numbers m such that the discriminant of the quadratic field Q(sqrt(m)) < m.

4, 9, 16, 18, 20, 25, 27, 32, 36, 45, 48, 49, 50, 52, 54, 63, 64, 68, 72, 75, 80, 81, 84, 90, 96, 98, 99, 100, 108, 112, 116, 117, 121, 125, 126, 128, 132, 135, 144, 147, 148, 150, 153, 160, 162, 164, 169, 171, 175, 176, 180, 189, 192, 196, 198, 200, 207, 208, 212

Offset: 1

Author

Benoit Cloitre, Aug 10 2002

Keywords

• easy
• nonn

Comments

Among terms are all the squares for which discriminant = 1.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037449, A072904.

Programs

Mathematica

Select[Range[220], NumberFieldDiscriminant[Sqrt[#]] < # &] (* Amiram Eldar, Jun 24 2022 *)

PARI

isok(m) = quaddisc(m) < m; \\ Michel Marcus, Feb 18 2021

Formula

a(n) appears to be asymptotic to C*n with C = 3.4... .