Erdős Problem #1139 — Unbounded Gaps Between Almost-Primes

Let $1 \leq u_0<u_1<u_2<\cdots$ be the increasing sequence of positive integers having at most two prime factors, counted with multiplicity. Is

$$\limsup_{k\to\infty}\frac{u_{k+1}-u_k}{\log(k+1)}=\infty?$$