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 A317990 #13 Mar 31 2019 04:08:55 %S A317990 1,2,1,2,2,2,2,1,2,4,1,2,2,2,2,2,1,4,2,2,2,4,1,2,4,1,4,2,2,2,4,1,4,2, %T A317990 2,2,1,2,2,4,2,2,4,2,1,2,2,4,2,2,2,2,2,4,1,4,2,2,4,1,1,4,2,4,2,2,1,4, %U A317990 4,1,4,4,2,4,2,4,2,2,4,2,2,2,1,4,2,2,2 %N A317990 Number of genera of real quadratic field Q(sqrt(k)), k squarefree > 1. %C A317990 The number of genera of a quadratic field is equal to the number of elements x in the class group such that x^2 = e where e is the identity. %C A317990 This is the analog of A003643 for real quadratic fields. Note that for this case "the class group" refers to the narrow class group, or the form class group of indefinite binary forms with discriminant k. %H A317990 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 A317990 a(n) = 2^(omega(A005117(n)-1)) = 2^A317992(n), where omega(k) is the number of distinct prime divisors of k. %o A317990 (PARI) for(n=2, 200, if(issquarefree(n), print1(2^(omega(n*if(n%4>1, 4, 1)) - 1), ", "))) %Y A317990 Cf. A003643, A005117, A087048, A317989, A317992. %K A317990 nonn %O A317990 2,2 %A A317990 _Jianing Song_, Oct 03 2018 %E A317990 Offset corrected by _Jianing Song_, Mar 31 2019