We have performed a temperature-dependent angle-integrated photoemission study of lightly-doped to heavily-overdoped La$_{2-x}$Sr$_{x}$CuO$_4$ and oxygen-doped La$_2$CuO$_{4.10}$. We found that both the magnitude $Delta$* of the (small) pseudogap and the temperature textit{T}* at which the pseudogap is opened increases with decreasing hole concentration, consistent with previous studies. On the other hand, the superconducting gap $Delta_{sc}$ was found to remain small for decreasing hole concentration. The results can be explained if the superconducting gap opens only on the Fermi arc around the nodal (0,0)-($pi,pi$) direction while the pseudogap opens around $sim$($pi$, 0).
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