Search: id:A107861
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%I A107861
%S A107861 2,3,7,9,31,19,127,81,343,211,2047,361,8191,2059,14221,6561,131071,6859,
%T A107861 524287,44521,778765,175099,8388607,130321,28629151,1586131,40353607,
%U A107861 4239481,536870911,1360291,2147483647,43046721
%N A107861 Number of unique values in the sums of all subsets of the n-th roots 
               of unity.
%C A107861 Note that a(6)=19, a(12)=19^2 and a(18)=19^3. Similarly, a(10)=211 and 
               a(20)=211^2. For prime n, a(n)=2^n-1. For powers of 2, we have a(2^n)=3^(2^(n-1)). 
               It appears David W. Wilson's conjectured formula for A103314 may 
               apply to this sequence also. Observe that due to symmetry, n divides 
               a(n)-1.
%H A107861 T. D. Noe, <a href="http://www.sspectra.com/math/RootSums.html">Sums 
               of Roots of Unity Plots</a>
%e A107861 a(1)=2 as there are two distinct sums: the sum of empty subset of roots 
               is 0 and the sum of {1} is 1.
%o A107861 { a(n) = local(S=Set()); forvec(c=vector(n,i,[0,1]), S=setunion(S,[Pol(c)%polcyclo(n)])); 
               length(S) } (Max Alekseyev)
%Y A107861 Cf. A103314 (number of subsets of the n-th roots of unity summing to 
               zero).
%Y A107861 Sequence in context: A057239 A024541 A123481 this_sequence A109800 A152136 
               A059180
%Y A107861 Adjacent sequences: A107858 A107859 A107860 this_sequence A107862 A107863 
               A107864
%K A107861 nonn
%O A107861 1,1
%A A107861 T. D. Noe (noe(AT)sspectra.com), May 25 2005
%E A107861 a(1) corrected by Max Alekseyev, Jun 25 2007
%E A107861 a(21)-a(32) from Max Alekseyev (maxale(AT)gmail.com), Sep 07 2007

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