  We investigate properties of a multivariate function $E(m_1,m_2,...,m_r)$,
called {\it orbicyclic}, that arises in enumerative combinatorics in counting
non-isomorphic maps on orientable surfaces. $E(m_1,m_2,...,m_r)$ proves to be
multiplicative, and a simple formula for its calculation is provided. It is
shown that the necessary and sufficient conditions for this function to vanish
is equivalent to familiar Harvey's conditions that characterize possible
branching data of finite cyclic automorphism groups of Riemann surfaces.
