  We consider the values taken by $n\times n$ circulant determinants with
integer entries when $n$ is the product of two distinct odd primes $p,q$. These
correspond to the integer group determinants for $\mathbb Z_{pq}$, the cyclic
group of order $pq$. We show that $p^2$ and $q^2$ are not determinants (more
generally we show that the classic necessary divisibility conditions are never
sufficient when $n$ contains at least two odd primes). We obtain a complete
description of the integer group determinants for $\mathbb Z_{15}$ (the
smallest unresolved group) and partial results for general $n=3p.$
