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A107848 Number of subsets of the n-th roots of unity summing to a real number. 3

%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 n-th 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 n-th roots of unity summing to zero).

%K nonn

%O 1,1

%A _T. D. Noe_, May 25 2005

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Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)