Erdős Problem #49 — Longest sequence in $[1,n]$ with increasing $\varphi$ values

Let $a_1, \ldots, a_t$ be the longest sequence for which

$$a_1 < \cdots < a_t \leq n \quad \text{and} \quad \varphi(a_1) < \cdots < \varphi(a_t).$$

Probably $t = \pi(n)$. Can one even prove $t < (1 + o(1))\pi(n)$ or at least $t = o(n)$? This latest conjecture will probably be easy. Similar questions can be posed about $\sigma(n)$.