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A094619 Fundamental discriminants of real quadratic number fields with class number 2.

%I A094619 #23 Feb 16 2025 08:32:53
%S A094619 40,60,65,85,104,105,120,136,140,156,165,168,185,204,205,220,221,232,
%T A094619 264,265,273,280,285,296,305,312,345,348,357,364,365,377,380,385,408,
%U A094619 424,429,440,444,456,460,465,476,481,485,488,492,493,533,545,552,561,565
%N A094619 Fundamental discriminants of real quadratic number fields with class number 2.
%H A094619 Charles R Greathouse IV, <a href="/A094619/b094619.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H A094619 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%H A094619 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A094619 Select[Range[565], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 2 &] (* _Arkadiusz Wesolowski_, Oct 22 2012 *)
%o A094619 (PARI) is(n)=n>9 && isfundamental(n) && qfbclassno(n)==2 \\ _Charles R Greathouse IV_, Nov 05 2014
%o A094619 (Sage)
%o A094619 is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 2;
%o A094619 A094619 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
%o A094619 A094619(600) # _G. C. Greubel_, Mar 01 2019
%Y A094619 Cf. A003656, A094612-A094614, A218156-A218160.
%K A094619 nonn
%O A094619 1,1
%A A094619 _Eric W. Weisstein_, May 14 2004