Discussions can be found in [24]-[32]. Similar investigation to test the particular scenario of coupled quintessence model by using the cluster number counts was investigated in [34–36], where the interaction between quintessence and DM was specifically described by some product of the densities of DE and DM. The sign they used for the coupling between dark sectors just describes the energy decay from DM to DE and they concentrated on the inhomogeneities in the DM fluid propagating in the scalar field and affecting the scalar field evolution. The cluster number counts dependence on the amount of DM coupled to DE was analyzed therein. In this paper we will investigate the possibility of employing measurements from cluster number counts to grasp the signature of interactions between DE and DM in some commonly discussed phenomenological models. These models were proved to have stable curvature perturbations [8] and have been tested by confronting CMB [17] and virial mass of cluster observations [23]. In our study we will use the spherical collapse model and consider either DE being distributed homogeneously or inhomogeneously. We will discuss the dynamics of DM and the inhomogeneous DE to virialization. When DE is homogeneous, DM flows to equilibrium in agreement with that discussed in [38] if there is no interaction between dark sectors. If the DE is inhomogeneous, we will show that its dynamics is different from that of DM in the virialization in the linear perturbation level. This indicates that DE does not cluster fully along with the DM and thus energy is not strictly conserved inside the collapsing system in the linear perturbation theory. Our result is a progress in the linear perturbation formalism, which has not been reported before. In the following discussion of this work, we will use the Press and Schechter formalism [39] to predict the number density of collapsed objects. We will develop a new treatment on studying how the structure is formed when DE does not trace DM. The Press and Schechter formalism is crude if compared with N-body simulations, while here we do not seek the precise confrontations with the observational data, but the evolution of the mass function of collapsed objects predicted by the formalism will be helpful for us to understand the influence of the interaction between dark sectors and the inhomogeneous DE distribution on cluster number counts. This paper is organized as follows: In Section II, we review the formalism of the perturbation theory in the presence of interaction between dark sectors. In Section III, we study the dynamics to describe the flow of the collapsing object to virialization. In Section IV, we introduce the spherical collapse model in the presence of coupling between DE and DM and the Press-Schechter formalism for the galaxy number counts. In Section V, we show the numerical results on how the interaction and inhomogeneous DE influence the cluster number counts. In the last section we present our summary and discussions. 3