0 1 2 3 4 1.2 1.4 1.6 1.8 2 W=−1.04, $_{1}$= $_{2}$,Ce$^{2}$=1 CDM =0.0001 =0.0001 =0.0003 =0.0003 =0.0005 =0.0005 z c 0 1 2 3 4 2 4 6 8 10 W=−1.04, $_{1}$= $_{2}$,Ce$^{2}$=1 CDM =0.0001 =0.0001 =0.0003 =0.0003 =0.0005 =0.0005 z c /  8 D(z) (a) (b) 0 1 2 3 4 5 10 15 20 25 30 35 40 W=−1.04, $_{1}$= $_{2}$,Ce$^{2}$=1 fixed  8 CDM =0.0001 =0.0001 =0.0003 =0.0003 =0.0005 =0.0005 10$^{13}$<M/(h$^{−1}$M$_{s}$)<10 14 z dN/dz/10 6 0 1 2 3 4 50 100 150 W=−1.04, $_{1}$= $_{2}$,Ce$^{2}$=1 fixed  8 CDM =0.0001 =0.0001 =0.0003 =0.0003 =0.0005 =0.0005 10$^{14}$<M/(h$^{−1}$M$_{s}$)<10 15 z dN/dz/10 4 Figure 4: The numerical results for the coupling proportional to the energy density of total dark sectors. The solid lines shows the results calculated with homogeneous DE distribution and the dotted lines are for inhomogeneous DE. cosmological constant model due to the interaction between DE and DM (solid lines) is suppressed if compared with the result by fixing σ$_{8}$ Fig 3. This shows that fixing the halo abundance, the coupling does not show up in the galaxy number counts. However, in this case, the difference caused by the clustering DE (dotted lines) is enhanced with large deviations from the cosmological constant model. When the coupling is proportional to the energy density of total dark sectors, the qualitative results are the same. 18