cp's OEIS Frontend

A316743 Discriminants of imaginary fields whose class group has exponent 2, negated.

%I A316743 #16 Feb 03 2025 22:48:30
%S A316743 15,20,24,35,40,51,52,84,88,91,115,120,123,132,148,168,187,195,228,
%T A316743 232,235,267,280,312,340,372,403,408,420,427,435,483,520,532,555,595,
%U A316743 627,660,708,715,760,795,840,1012,1092,1155,1320,1380,1428,1435,1540,1848,1995,2280,3003,3315,5460
%N A316743 Discriminants of imaginary fields whose class group has exponent 2, negated.
%C A316743 This sequence lists the negated discriminants of imaginary fields whose class group is isomorphic to (C_2)^r, r > 0.
%C A316743 These are the negated fundamental discriminants in A133288.
%C A316743 Also numbers in A003644 but not in A014602. Equals A014603 union A192322 union A305416 union {5460}.
%H A316743 Shin-ichi Katayama, <a href="https://www.researchgate.net/publication/387687885_Rational_Points_on_the_Parabola_and_the_Arithmetic_of_Related_Algebraic_Tori">Rational Points on the Parabola and the Arithmetic of Related Algebraic Tori</a>, J. Math. Tokushima Univ. (2024) Vol. 58, 11-31. See p. 30.
%H A316743 Rick L. Shepherd, <a href="http://libres.uncg.edu/ir/uncg/f/Shepherd_uncg_0154M_11099.pdf">Binary quadratic forms and genus theory</a>, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
%H A316743 P. J. Weinberger, <a href="http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-aav22i2p117bwm">Exponents of the class groups of complex quadratic fields</a>, Acta Arith. 22 (1973), 117-124.
%o A316743 (PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no > 1 && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ _Andrew Howroyd_, Jul 20 2018
%Y A316743 Cf. Negated discriminants of imaginary fields whose class group is isomorphic to (C_2)^r: A014602 (r=0), A014603 (r=1), A192322 (r=2), A305416 (r=3).
%Y A316743 Subsequence of A003644 and A133288.
%K A316743 nonn,fini,full
%O A316743 1,1
%A A316743 _Jianing Song_, Jul 20 2018