%I
%S 0,0,1,0,0,1,1,1,0,1,0,1,0,1,0,1,1,2,0,1,1,0,1,1,1,1,0,1,1,0,0,1,2,0,
%T 0,2,1,1,1,1,0,2,1,1,0,1,2,0,1,2,2,1,0,1,0,1,1,1,0,0,1,2,1,1,1,1,2,1,
%U 0,1,0,1,1,0,1,1,1,0,2,1,1,0,2,0,2,0,1
%N 2rank of the class group of real quadratic field with discriminant A003658(n), n >= 2.
%C The prank of a finite abelian group G is equal to log_p(#{x belongs to G : x^p = 1}) where p is a prime number. In this case, G is the narrow class group of Q[sqrt(k)] or the form class group of indefinite binary quadratic forms with discriminant k, and #{x belongs to G : x^p = 1} is the number of genera of Q[sqrt(k)] (cf. A317989).
%C This is the analog of A319659 for real quadratic fields.
%H Rick L. Shepherd, <a href="https://libres.uncg.edu/ir/uncg/listing.aspx?id=15057">Binary quadratic forms and genus theory</a>, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
%F a(n) = omega(A003658(n))  1 = log_2(A317989(n)), where omega(k) is the number of distinct prime divisors of k.
%t PrimeNu[Select[Range[2, 300], NumberFieldDiscriminant[Sqrt[#]] == #&]]  1 (* _JeanFrançois Alcover_, Jul 25 2019 *)
%o (PARI) for(n=2, 1000, if(isfundamental(n), print1(omega(n)  1, ", ")))
%Y Cf. A003658, A087048, A317989, A317992, A319659.
%K nonn
%O 2,18
%A _Jianing Song_, Oct 03 2018
%E Offset corrected by _Jianing Song_, Mar 31 2019
