Erdős problem 648

Let $g(n)$ denote the largest $t$ such that there exist integers $2\leq a_1<a_2<\cdots <a_t <n$ such that $$P(a_1)>P(a_2)>\cdots >P(a_t)$$ where $P(m)$ is the greatest prime factor of $m$. Estimate $g(n)$.