The sigma meson production in p + ~(12)C and p + ~(40)Ca reactions at the incident energy E_p=1.5 GeV isinvestigated within the Quantum Molecular Dynamics model.The simulation results indicate a distinctive A dependenceof the sigma production,that is,the increase of A is followed by an increase of the production cross sections.We findthat the σ meson production in proton-induced reactions is strongly medium-dependent,and the produced σ mesonsdecaying in a denser medium experience a stronger mass shift towards lower masses.This mass shift is an experimentallyaccessible observable in the final state pion pairs,which do not suffer from reabsorption by the surrounding nucleons.It is pointed out that the ratio of measured sigma cross sections as a function of the sigma invariant-mass from variousreactions is a good probe to explore the existence of the a meson in a dense nuclear environment. The sigma meson production in p + ~ (12) C and p + ~ (40) Ca reactions at the incident energy E_p = 1.5 GeV is investigated within the Quantum Molecular Dynamics model. The simulation results indicate a distinctive A dependence of the sigma production, that is, the increase of A is followed by an increase of the production cross sections. We find that the σ meson production in proton-induced reactions is strongly medium-dependent, and the produced σ mesons decay in a denser medium experience a stronger mass shift towards lower masses. This mass shift is an experimentally accessible observable in the final state pion pairs, which do not suffer from reabsorption by the surrounding nucleons. It is pointed out that the ratio of measured sigma cross sections as a function of the sigma invariant-mass from various actions is a good probe to explore the existence of the a meson in a dense nuclear environment.