The oxygen-isotope effect on the ferromagnetic transition temperature ${T}_{C}$ has been studied on the manganites ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3+y}$ as a function of x. As x increases, both the oxygen-isotope exponent ${\ensuremath{\alpha}}_{\mathrm{O}}$ and the pressure-effect coefficient $\ensuremath{\beta}=d\mathrm{ln}{T}_{C}/dP$ increase, reach a maximum at a composition near the metal-insulator phase boundary ${x}_{\mathrm{MI}},$ and then decrease monotonically. For ${x}_{\mathrm{MI}}<x<0.33,$ the isotope exponent follows: ${\ensuremath{\alpha}}_{\mathrm{O}}=21.9\mathrm{exp}(\ensuremath{-}{0.016T}_{C}),$ which is simply proportional to $\ensuremath{\beta}.$ The present results demonstrate that the observed oxygen-isotope effect is an intrinsic property of manganites, which arises from a strong electron-phonon coupling.