  We study a class of models in which the inflaton is minimally coupled to
gravity with a term $f(R)\vp^2$. We focus in particular on the case when $f\sim
R^2$, the expansion of the scale factor is driven by the usual potential
energy, while the rolling of the inflaton is driven by the nonminial coupling.
We show that the power spectrum is in general blue, and the problem of getting
a running spectral index is eased. However, the inflaton potential must have a
large second derivative in order to get a large running.
