Search: id:A002143
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%I A002143 M2266 N0896
%S A002143 1,1,1,1,3,3,1,5,3,1,7,5,3,5,3,5,5,3,7,1,11,5,13,9,3,7,5,15,7,13,11,3,
%T A002143 3,19,3,5,19,9,3,17,9,21,15,5,7,7,25,7,9,3,21,5,3,9,5,7,25,13,5,13,3,
%U A002143 23,11,5,5,31,13,5,21,15,5,7,9,7,33,7,21,3,29,3,31,19,5,11,15,27,17,13
%N A002143 Class numbers h(-p) where p runs though the primes p == 3 (mod 4).
%C A002143 a(n) = h(-A002145(n)).
%D A002143 E. T. Ordman, Tables of the class number for negative prime discriminants, 
               Math. Comp., 23 (1969), 458.
%D A002143 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002143 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002143 T. D. Noe, <a href="b002143.txt">Table of n, a(n) for n=1..10000</a>
%H A002143 Kevin A. Broughan, <a href="http://www.math.waikato.ac.nz/~kab/papers/
               div4.pdf">Restricted divisor sums</a>, Acta Arithmetica, vol. 101, 
               (2002), pp. 105-114.
%H A002143 N. Snyder, <a href="http://math.berkeley.edu/~nsnyder/tutorial/lecture7.pdf">
               Lectures # 7: The Class Number Formula For Positive Definite Binary 
               Quadratic Forms.</a> [Background information on class numbers, link 
               sent by V. S. Miller, Nov 22 2009]
%H A002143 Wikipedia, <a href="http://en.wikipedia.org/wiki/Class_number_(number_theory)#Class_numbers_of_quadratic_fiel\
               ds">Class numbers of quadratic fields</a>
%F A002143 h(-p) = 1 + 2*sum(0 <= n <= (1/2)*sqrt(p/3)-1, d(n^2+n+(p+1)/4, [2*n+1, 
               sqrt(n^2+n+(p+1)/4)])) for prime p=3 mod 4, p>3. d(n, [a, b])=card{d: 
               d|n and a<d<b} for integer n and real a, b. - Antonio G. Astudillo 
               (afg_astudillo(AT)hotmail.com), Jul 19 2002
%e A002143 E.g. a(4) = 1 is the class number of -19, the 4-th prime == 3 mod 4
%Y A002143 Cf. A002145 (primes p), A002146
%Y A002143 Sequence in context: A111408 A092674 A111945 this_sequence A039739 A160496 
               A105663
%Y A002143 Adjacent sequences: A002140 A002141 A002142 this_sequence A002144 A002145 
               A002146
%K A002143 nonn,new
%O A002143 1,5
%A A002143 N. J. A. Sloane (njas(AT)research.att.com).
%E A002143 More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), 
               Jul 19 2002
%E A002143 Editorial comments from M. F. Hasler, Nov 22 2009

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