Erdős Problem 370

Reference: erdosproblems.com/370

theorem erdos_370 : {n : ℕ | ↑n.maxPrimeFac < √↑n ∧ ↑(n + 1).maxPrimeFac < √(↑n + 1)}.Infinite ↔ True

Are there infinitely many $n$ such that the largest prime factor of $n$ is $< n^{\frac{1}{2}}$ and the largest prime factor of $n + 1$ is $< (n + 1)^{\frac{1}{2}}$.

Steinerberger has pointed out this problem has a trivial solution.