cp's OEIS Frontend

A003641 Number of genera of imaginary quadratic field with discriminant -k, k = A039957(n).

%I A003641 M0061 #20 Jul 25 2019 16:58:09
%S A003641 1,1,1,2,1,1,1,2,2,1,1,2,2,1,1,1,1,1,2,2,2,1,1,2,2,2,2,1,1,1,2,1,2,2,
%T A003641 1,1,1,2,2,1,4,1,2,1,2,2,1,1,4,2,1,2,1,4,2,1,2,1,1,2,2,2,2,2,1,1,2,2,
%U A003641 2,1,2,2,1,2,1,1,2,1,1,2,2,4,2,2,2,2,1,2,1,4,1,1,2,2,4,1,1,2,1,4,1,1,1,1,2
%N A003641 Number of genera of imaginary quadratic field with discriminant -k, k = A039957(n).
%C A003641 In other words, this is the number of genera of those imaginary quadratic fields that have a discriminant which is odd and fundamental. The discriminant will be squarefree and of the form -4n+1. - _Andrew Howroyd_, Jul 25 2018
%D A003641 D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.
%D A003641 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003641 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%F A003641 a(n) = 2^(omega(A039957(n)) - 1). - _Jianing Song_, Jul 24 2018
%e A003641 a(4) = 2 because -15 = -A039957(4) and the number of genera of the quadratic field with discriminant -15 is 2. - _Andrew Howroyd_, Jul 25 2018
%t A003641 2^(PrimeNu[Select[Range[1000], Mod[#, 4] == 3 && SquareFreeQ[#]&]] - 1) (* _Jean-François Alcover_, Jul 25 2019, after _Andrew Howroyd_ *)
%o A003641 (PARI) for(n=1, 1000, if(n%4==3 && issquarefree(n), print1(2^(omega(n) - 1), ", "))) \\ _Andrew Howroyd_, Jul 24 2018
%Y A003641 Cf. A001221 (omega), A003640, A003642, A039957.
%K A003641 nonn
%O A003641 1,4
%A A003641 _N. J. A. Sloane_, _Mira Bernstein_
%E A003641 Name clarified by _Jianing Song_, Jul 24 2018