  We show that pure quadratic gravity with quantum loop corrections yields a
viable inflationary scenario. We also show that a large family of models in the
Jordan frame, with softly-broken scale invariance, corresponds to the same
theory with linear inflaton potential in the Einstein frame. It follows that
all these quasi scale-invariant models have the same relation between the
tensor-to-scalar ratio and the scalar spectral index, which is also consistent
with the current data. Thus, they form a family of attractors, which is sharply
distinct from the recently discovered $\alpha$-attractors of Kallosh, Linde et
al.
