ATLAS results on charmonium production and $B_c^+$ meson production and decays

Recent results from the proton-proton collision data taken by the ATLAS experiment on the charmonium production and on the $B_c^+$ meson production and decays are presented. The measurement of $J/\psi$ meson and $\psi(2S)$ meson differential cross sections is reported. New results on the $B_c^+$ meson decays to $J/\psi D_s^{(*)}$ final states are included. Both studies are based on $pp$ collision data collected at $\sqrt{s}=13$ TeV during the LHC Run 2, corresponding to an integrated luminosity of 139 $fb^{-1}$. The measurement of the differential ratios of the $B_c^+$ and $B^+$ mesons production cross sections at $\sqrt{s}=8$ ~TeV with an integrated luminosity of 20.3$fb^{-1}$ is also discussed.