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 A317992 #17 Feb 24 2021 08:16:59
%S A317992 0,1,0,1,1,1,1,0,1,2,0,1,1,1,1,1,0,2,1,1,1,2,0,1,2,0,2,1,1,1,2,0,2,1,
%T A317992 1,1,0,1,1,2,1,1,2,1,0,1,1,2,1,1,1,1,1,2,0,2,1,1,2,0,0,2,1,2,1,1,0,2,
%U A317992 2,0,2,2,1,2,1,2,1,1,2,1,1,1,0,2,1,1,1
%N A317992 2-rank of the narrow class group of real quadratic field Q(sqrt(k)), k squarefree > 1.
%C A317992 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. A317990).
%C A317992 This is the analog of A319662 for real quadratic fields.
%H A317992 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 A317992 a(n) = omega(A005117(n)) - 1 = log_2(A317990(n)), where omega(k) is the number of distinct prime divisors of k.
%o A317992 (PARI) for(n=2, 200, if(issquarefree(n), print1(omega(n*if(n%4>1, 4, 1)) - 1, ", ")))
%Y A317992 Cf. A005117, A087048, A317990, A317991, A319662.
%K A317992 nonn
%O A317992 2,10
%A A317992 _Jianing Song_, Oct 03 2018
%E A317992 Offset corrected by _Jianing Song_, Mar 31 2019