%I A105609
%S A105609 1,0,1,2,1,3,1,2,1,5,1,1,1,7,1,2,1,3,1,1,1,11,1,1,1,13,1,1,1,1,1,2,1,17,
%T A105609 1,1,1,19,1,1
%V A105609 1,0,-1,-2,1,-3,-1,2,-1,5,-1,1,1,-7,1,2,1,-3,-1,1,1,-11,-1,1,1,13,-1,1,
               1,1,-1,2,1,17,1,
%W A105609 1,1,-19,1,1
%N A105609 Sylvester numbers for 1/(1+x^2).
%H A105609 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SylvesterCyclotomicNumber.html">Sylvester Cyclotomic Number</a>.
%F A105609 a(n)=product{k=1..n-1, if(gcd(n, k)=1, (I+I*exp(2*pi*I*k/n), 1)}, I=sqrt(-1)
%e A105609 (x+I)(x-I)=1+x^2
%t A105609 f[n_] := FullSimplify[ Expand[Times @@ (I + I*Exp[2Pi*I*Select[Range[n], 
               GCD[ #, n] == 1 &]/n])]]; Table[ f[n], {n, 0, 32}] (from Robert G. 
               Wilson v (rgwv(AT)rgwv.com), Aug 02 2005)
%Y A105609 Cf. A020513, A105608, A105607.
%Y A105609 Sequence in context: A065704 A026100 A059127 this_sequence A101872 A069929 
               A101312
%Y A105609 Adjacent sequences: A105606 A105607 A105608 this_sequence A105610 A105611 
               A105612
%K A105609 easy,sign,more
%O A105609 0,4
%A A105609 Paul Barry (pbarry(AT)wit.ie), Apr 15 2005