Recently it was proposed that a very small oxygen-isotope effect in the high-Tc Cu oxides can be understood in terms of a logarithmic singularity in the density of states, N (E), near the Fermi energy, along with a conventional BCS phonon-mediated pairing. In this paper we show that a relatively realistic N (E), derived from a tight-binding model on two-dimensional lattices, contains a logarithmic term plus a constant term. The calculated result indicates that the additional constant term in N (E) makes the minimum for the isotope-mass exponent a well exceed the corresponding experimental value (a～0-0.2). The interplanar hopping is shown to smear out the sharp peak of N (E) so that a shifts further towards the standard BCS value of 2/1. So it appears to us that an explanation of the isotope effect as a function of doping in terms of a Van Hove singularity is not tenable.