A107753 Number of primitive subsets of the n-th roots of unity summing to zero.

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

Offset: 1

Author

T. D. Noe, May 23 2005

Keywords

• nonn

Comments

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.

Crossrefs

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).

Formula

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.