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 A319661 2-rank of the class group of imaginary quadratic field with discriminant -k, k = A191483(n). 2
 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 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 class group of Q(sqrt(-k)), and #{x belongs to G : x^p = 1} is the number of genera of Q(sqrt(-k)) (cf. A003642). LINKS Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013. FORMULA a(n) = log_2(A003642(n)) = omega(A191483(n)) - 1, where omega(k) is the number of distinct prime divisors of k. MATHEMATICA PrimeNu[Select[Range[1000], Mod[#, 4] == 0 && SquareFreeQ[#/4] && Mod[#, 16] != 12&]] - 1 (* Jean-François Alcover, Aug 02 2019, after Andrew Howroyd in A191483 *) PROG (PARI) for(n=1, 1000, if(isfundamental(-n) && n%2==0, print1(omega(n) - 1, ", "))) (Sage) def A319661_list(len): L = [] for n in range(2, len+1, 2): if is_fundamental_discriminant(-n): L.append(sloane.A001221(n) - 1) return L print(A319661_list(854)) # Peter Luschny, Oct 15 2018 CROSSREFS Cf. A003642, A191483, A319659, A319660. Sequence in context: A294338 A316790 A316789 * A320015 A342956 A241918 Adjacent sequences: A319658 A319659 A319660 * A319662 A319663 A319664 KEYWORD nonn AUTHOR Jianing Song, Sep 25 2018 STATUS approved

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Last modified March 24 07:49 EDT 2023. Contains 361454 sequences. (Running on oeis4.)