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

1,2

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.

Links

Table of n, a(n) for n=1..41.

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.

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).

Sequence in context: A329607 A108499 A260895 * A197929 A326849 A328706

Adjacent sequences: A107750 A107751 A107752 * A107754 A107755 A107756

Keyword

nonn

Author

T. D. Noe, May 23 2005

Status

approved