%I
%S 2,4,4,8,8,24,16,48,40,144,64,336,128,864,416,1728,512,8304,1024,
%T 10656,4032,31104,4096,116256,9248,186624,40000,374976,32768,3537024,
%U 65536,2239488
%N Number of subsets of the nth roots of unity summing to a real number.
%H T. D. Noe, <a href="http://www.sspectra.com/math/RootSums.html">Sums of Roots of Unity Plots</a>
%F For prime n, a(n)=2^((n+1)/2).
%t Needs["DiscreteMath`Combinatorica`"]; Table[Plus@@Table[Count[(KSubsets[Range[n], k]), q_List/;Im[Chop[Plus@@(E^(2.*Pi*I*q/n))]]==0], {k, 0, n}], {n, 20}]
%Y Cf. A103314 (number of subsets of the nth roots of unity summing to zero).
%K nonn
%O 1,1
%A _T. D. Noe_, May 25 2005
