A107753 - OEIS

%I #2 Mar 30 2012 17:22:40

%S 1,2,2,3,2,6,2,5,4,8,2,11,2,10,9,9,2,16,2,15,11,14,2,21,6,16,10,19,2,

%T 212,2,17,15,20,13,31,2,22,17,29,2

%N Number of primitive subsets of the n-th roots of unity summing to zero.

%C A primitive subset has no nonempty proper subset whose members sum to zero. Note that a(30) is the first term for which the formulas do not apply. For n=30, there are 1,0,15,10,0,5,30,60,60,30 primitive subsets of size 0,1,2,...,9.

%F For primes p and q, if n = p^i, then a(n)=1+n/p; if n=p^i q^j, then a(n)=1+n/p+n/q.

%Y Cf. A103314 (number of subsets of the n-th roots of unity summing to zero), A107754 (number of subsets of the n-th roots of unity summing to one).

%K nonn

%O 1,2

%A _T. D. Noe_, May 23 2005