The weaker inhomogeneous Duffin–Schaeffer conjecture

Let $$ be the inhomogeneous Duffin–Schaeffer statement referred to as , and let be the additional divergence condition referred to as . Weaker inhomogeneous Duffin–Schaeffer conjecture. Statement $$ holds if additionally $$ is satisfied for infinitely many $Q \text{.}$ This is presented as a weaker version of Ramírez's inhomogeneous Duffin–Schaeffer conjecture. The source states that even this version remains open and would be of interest.