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In this work, we demonstrate that optical pulling forces (OPFs) can be induced by a hybrid dimer consisting of a Si nanoparticle (NP) and a coated nanoparticle with a gain core and Au shell under normal plane wave illumination. Analytical theory reveals that the underlying physical mechanism relies on interactions between the electric dipole (ED) modes excited in the NPs. As compared with the individual NP, it is found that the magnitude of optical force can be enlarged by almost three orders for the Si NP and one order for the coated gain NP in the coupled dimer. In addition, we find that the OPFs exerted on the NPs are heavily dependent on the gain level of the core materials, the incident polarization angle and the sizes of the NPs. More interestingly, we find that the OPF can also be exerted on a trimer system consisting of two identical Si NPs and a coated NP arranged in a line. The related results could be used to propose a versatile platform for manipulating NPs.