Representation of an integer as a prime plus a product of two small factors

Let 35<θ<1. In this note, we will show that there exist n0=n0(θ) and δ=δ(θ)>0 such that every n≥n0 is representable as n=p+ab with p prime and integers a,b satisfying 1≤a,b≤n12−δ and ab≤nθ. This is an improvement of D.R. Health-Brown's result.