This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A317991 #21 Feb 24 2021 08:16:51
%S A317991 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 A317991 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 A317991 0,1,0,1,1,0,1,1,1,0,2,1,1,0,2,0,2,0,1
%N A317991 2-rank of the narrow class group of real quadratic field with discriminant A003658(n), n >= 2.
%C A317991 The p-rank 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 A317991 This is the analog of A319659 for real quadratic fields.
%H A317991 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 A317991 a(n) = omega(A003658(n)) - 1 = log_2(A317989(n)), where omega(k) is the number of distinct prime divisors of k.
%t A317991 PrimeNu[Select[Range[2, 300], NumberFieldDiscriminant[Sqrt[#]] == #&]] - 1 (* _Jean-François Alcover_, Jul 25 2019 *)
%o A317991 (PARI) for(n=2, 1000, if(isfundamental(n), print1(omega(n) - 1, ", ")))
%Y A317991 Cf. A003658, A087048, A317989, A317992, A319659.
%K A317991 nonn
%O A317991 2,18
%A A317991 _Jianing Song_, Oct 03 2018
%E A317991 Offset corrected by _Jianing Song_, Mar 31 2019