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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 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A037449.

Cf. A002144, A018252, A003658.

Sequence in context: A354069 A350615 A300065 * A269705 A189322 A105571

Adjacent sequences:  A072899 A072900 A072901 * A072903 A072904 A072905

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Aug 10 2002

STATUS

approved

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Last modified November 26 04:03 EST 2022. Contains 358353 sequences. (Running on oeis4.)