Given $n$ a fixed integer we constuct the following sequence:
$a_0=n$, $a_i=\lfloor \frac{a_{i-1}(p_i-1)}{p_i}\rfloor$. For what values of $n$ do we have $a_{\pi(n)}=0$?
Computer calculation shows it holds for all $n\in\{2,3,\dots ,10^5\}$ except $2,4,6,10,12,16,28$. Can we prove it is true for sufficiently large $n$?