  We have studied the novel isotope effects on the pairing pseudogap in
underdoped and optimally doped cuprates within the large-polaron model and two
non-standard BCS-like approaches. We have shown that in the
intermediate-coupling regime the precursor pairing of large polarons occurs at
a mean-field temperature $T^{\ast}>T_{c}$ and the near-absent, sizable and very
large oxygen and copper isotope effects on $T^{\ast}$ exist in cuprates with
small and large Fermi surfaces. Our results for $T^{\ast}$, isotope shifts and
exponents in slightly underdoped and optimally doped cuprates are in
quantitative agreement with existing experiments and explain the discrepancy
between various experiments.
