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%I #15 Feb 24 2021 08:17:06
%S 0,0,0,0,0,1,0,1,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,2,1,1,1,1,0,1,0,
%T 1,1,1,1,2,1,0,0,2,1,0,1,1,0,1,1,1,0,1,0,2,0,1,1,1,0,2,0,1,0,1,1,1,0,
%U 0,2,2,1,1,0,1,1,1,0,2,1,2,0,2,1,0,2,2
%N 2-rank of the class group of imaginary quadratic field with discriminant -k, k = A003657(n).
%C 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 class group of Q(sqrt(-k)), and #{x belongs to G : x^p = 1} is the number of genera of Q(sqrt(-k)) (cf. A003640).
%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) = log_2(A003640(n)) = omega(A003657(n)) - 1, where omega(k) is the number of distinct prime divisors of k.
%o (PARI) for(n=1, 1000, if(isfundamental(-n), print1(omega(n) - 1, ", ")))
%Y Cf. A003640, A003657, A319660, A319661, A319662.
%Y Real discriminant case: A317991.
%K nonn
%O 1,27
%A _Jianing Song_, Sep 25 2018
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