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 A317991 2-rank of the class group of real quadratic field with discriminant A003658(n), n >= 2. 2
 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, 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, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 0, 2, 0, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,18 COMMENTS 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). This is the analog of A319659 for real quadratic fields. LINKS Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013. FORMULA a(n) = omega(A003658(n)) - 1 = log_2(A317989(n)), where omega(k) is the number of distinct prime divisors of k. MATHEMATICA PrimeNu[Select[Range[2, 300], NumberFieldDiscriminant[Sqrt[#]] == #&]] - 1 (* Jean-François Alcover, Jul 25 2019 *) PROG (PARI) for(n=2, 1000, if(isfundamental(n), print1(omega(n) - 1, ", "))) CROSSREFS Cf. A003658, A087048, A317989, A317992, A319659. Sequence in context: A113706 A279952 A054845 * A236853 A117163 A096863 Adjacent sequences:  A317988 A317989 A317990 * A317992 A317993 A317994 KEYWORD nonn AUTHOR Jianing Song, Oct 03 2018 EXTENSIONS Offset corrected by Jianing Song, Mar 31 2019 STATUS approved

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Last modified October 21 14:45 EDT 2019. Contains 328301 sequences. (Running on oeis4.)