We review the classical Fuller index which is a certain rational invariant count of closed orbits of a smooth vector field, and then explain how in the case of a Reeb vector field on a contact manifold $C$, this index can be equated to a Gromov-Witten invariant counting holomorphic tori in the locally conformally symplectic manifold $C \times S^1$. This leads us to prove a certain variant of the classical Seifert conjecture for the odd dimensional spheres.