A072902 Nonprime numbers m such that the discriminant of the quadratic field Q(sqrt(m)) equals m.

1, 8, 12, 21, 24, 28, 33, 40, 44, 56, 57, 60, 65, 69, 76, 77, 85, 88, 92, 93, 104, 105, 120, 124, 129, 133, 136, 140, 141, 145, 152, 156, 161, 165, 168, 172, 177, 184, 185, 188, 201, 204, 205, 209, 213, 217, 220, 221, 232, 236, 237, 248, 249, 253, 264, 265, 268

Offset: 1

Author

Benoit Cloitre, Aug 10 2002

Keywords

• easy
• nonn

Comments

A subset of the nonprime numbers (A018252).

Positive fundamental discriminants (A003658) that are not Pythagorean primes (A002144). - Paul Muljadi, Mar 30 2008

Links

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

Crossrefs

Cf. A037449.

Cf. A002144, A018252, A003658.

Programs

Mathematica

FundamentalDiscriminantQ[d_] := Module[{m, mod = Mod[d, 4]}, If[mod > 1, Return[False]]; If[mod == 1, Return[ SquareFreeQ[d] && d != 1]]; m = d/4; Return[ SquareFreeQ[m] && Mod[m, 4] > 1]]; Join[{1}, Select[ Range[270], !PrimeQ[#] && FundamentalDiscriminantQ[#]& ]] (* Jean-François Alcover, Jun 05 2012, after Eric W. Weisstein *)

PARI

isok(m) = !isprime(m) && (quaddisc(m) == m); \\ Michel Marcus, Feb 18 2021

Formula

a(n) appears to be asymptotic to C*n with C = 3.91... .