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