A107847 - OEIS

%I #7 Dec 26 2023 04:22:20

%S 1,1,2,3,6,9,18,30,56,99,186,333,630,1161,2182,4080,7710,14508,27594,

%T 52371,99858,190557,364722,698634,1342176,2580795,4971008,9586377,

%U 18512790,35786499,69273666,134215680,260300986,505286415,981706806

%N Related to sums of the n-th roots of unity: sums in a circular wedge (excluding the origin).

%C Consider the 2^n sums formed from all the subsets of the n-th roots of unity. The number A103314(n) tells how many of these sums are zero. The remaining sums fall into n wedges centered at the origin. The number a(n) gives the number of sums that fall into each wedge. Interestingly, a(n) coincides with A059966(n) when n is either p^k or pq for primes p and q.

%H Max Alekseyev and M. F. Hasler, <a href="/A107847/b107847.txt">Table of n, a(n) for n = 1..164</a>

%H T. D. Noe, <a href="http://www.sspectra.com/math/RootSums.html">Sums of Roots of Unity Plots</a>

%F a(n) = (2^n - A103314(n))/n.

%F a(n) = A001037(n) - A110981(n). - _Max Alekseyev_, Jan 14 2008

%Y Cf. A103314 (number of subsets of the n-th roots of unity summing to zero), A107848 (number of subsets of the n-th roots of unity summing to a real number).

%Y Cf. also A110981.

%K nonn

%O 1,3

%A _T. D. Noe_, May 25 2005