Search: id:A105345
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%I A105345
%S A105345 257,353,409,521,569,809,857,953,1129,1153,1201,1217,1249,1657,2113,
%T A105345 2137,2153,2273,2377,2521,2617,2633,2657,2729,2833,3209,3217,3761,3769,
%U A105345 4481,4993,5569,5801,5897,6217,6329,6449,6529,7177,7193
%N A105345 Primes p with class number h(-p) divisible by 16.
%C A105345 These are a proper subset of the primes of the form x^2+32y^2 whose class 
               numbers are divisible by 8.
%D A105345 Cohn, H. Introduction to the construction of class fields, Cambridge, 
               1985, pp. 147-151
%D A105345 Leonard, Philip A. and Williams, Kenneth S. On the divisibility of the 
               class numbers of Q(sqrt(-p)) and Q(sqrt(-2p)) by 16, Canadian Math 
               Bulletin,v.25 (1982), pp. 200-6
%e A105345 h(-257)=16: binary quadratic forms of discriminant -4(257) are x^2+257y^2, 
               2x^2+2xy+129y^2, 3x^2+-2xy+86y^2, 6x^2+-2xy+43y^2,9x^2+-4xy+29y^2, 
               7x^2+-6xy+38y^2, 14x^2+-6xy+19y^2, 13x^2+-8xy+21y^2, 17x^2+-14xy+18y^2 
               for 16 forms (the +- forms count twice)
%Y A105345 Sequence in context: A139653 A060879 A062382 this_sequence A060261 A158231 
               A070815
%Y A105345 Adjacent sequences: A105342 A105343 A105344 this_sequence A105346 A105347 
               A105348
%K A105345 nonn
%O A105345 1,1
%A A105345 John L. Drost (drost(AT)marshall.edu), Apr 30 2005

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