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A072902
Nonprime numbers m such that the discriminant of the quadratic field Q(sqrt(m)) equals m.
1
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
1,2
COMMENTS
A subset of the nonprime numbers (A018252).
Positive fundamental discriminants (A003658) that are not Pythagorean primes (A002144). - Paul Muljadi, Mar 30 2008
LINKS
FORMULA
a(n) appears to be asymptotic to C*n with C = 3.91... .
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 *)
PROG
(PARI) isok(m) = !isprime(m) && (quaddisc(m) == m); \\ Michel Marcus, Feb 18 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Aug 10 2002
STATUS
approved