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%I #24 Nov 21 2019 07:49:27
%S 3,4,7,8,11,12,16,19,27,28,43,67,163
%N Negative discriminants with form class number 1 (negated).
%C The list on p. 260 of Cox is missing -12, the list in Theorem 7.30 on p. 149 is correct. - _Andrew V. Sutherland_, Sep 02 2012
%C Let b(k) be the number of integer solutions of f(x,y) = k, where f(x,y) is the principal binary quadratic form with discriminant d<0 (i.e., f(x,y) = x^2 - (d/4)*y^2 if 4|d, x^2 + x*y + ((1-d)/4)*y^2 otherwise), then this sequence lists |d| such that {b(k)/b(1): k>=1} is multiplicative. See Crossrefs for the actual sequences. - _Jianing Song_, Nov 20 2019
%D D. A. Cox, Primes of the form x^2+ny^2, Wiley, New York, 1989, pp. 149, 260.
%D D. E. Flath, Introduction to Number Theory, Wiley-Interscience, 1989.
%o (PARI) ok(n)={(-n)%4<2 && quadclassunit(-n).no == 1} \\ _Andrew Howroyd_, Jul 20 2018
%Y Cf. A014602, A003173.
%Y The sequences {b(k): k>=0}: A004016 (d=-3), A004018 (d=-4), A002652 (d=-7), A033715 (d=-8), A028609 (d=-11), A033716 (d=-12), A004531 (d=-16), A028641 (d=-19), A138805 (d=-27), A033719 (d=-28), A138811 (d=-43), A318984 (d=-67), A318985 (d=-163).
%Y The sequences {b(k)/b(1): k>=1}: A002324 (d=-3), A002654 (d=-4), A035182 (d=-7), A002325 (d=-8), A035179 (d=-11), A096936 (d=-12), A113406 (d=-16), A035171 (d=-19), A138806 (d=-27), A110399 (d=-28), A035147 (d=-43), A318982 (d=-67), A318983 (d=-163).
%K fini,full,nonn,nice
%O 1,1
%A _N. J. A. Sloane_, May 16 2003
%E Corrected by _David Brink_, Dec 29 2007
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