In this paper we investigate the $eta_c$ production by photon - photon and photon - hadron interactions in $pp$ and $pA$ collisions at the LHC energies. The inclusive and diffractive contributions for the $eta_c$ photoproduction are estimated using the nonrelativistic quantum chromodynamics (NRQCD) formalism. We estimate the rapidity and transverse momentum distributions for the $eta_c$ photoproduction in hadronic collisions at the LHC and present our estimate for the total cross sections at the Run 2 energies. A comparison with the predictions for the exclusive $eta_c$ photoproduction, which is a direct probe of the Odderon, also is presented.
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