A103314 conjecture

[T. D. Noe]

>
>>  f(p) = 2 (obvious, either all or none) [f = A103314]
>
>Can you explain to me why it's obvious?

There is an interesting paper at http://arxiv.org/abs/math.NT/9511209
titled "On vanishing sums for roots of unity".  It corroborates the results
in A103306, which shows that if primes p1,..,pr divide n , then there are
subsets of size m1*p1+m2*p2+...+mr*pr that sum to zero for any nonnegative
integers m1,..,mr.

I wonder whether it would be useful to count the primitive subsets that sum
to zero; that is, subsets which have no subsets summing to zero.

Tony