While studying I've encountered this question written above.
I am familiar to the closure properties of CFL, and even know that $$L=\{a^{j^2}|j\geqslant 0\}$$ ($a$ to the power of ($j$ to the power of $2$))
is one that answers the question, but I don't know how to prove that.
If anyone could explain it to me, it would be excellent!
Thank you.
I think proving that $\text{Pref}(L)$ is CFL is the easiest part (it is even regular): ask yourself what are all prefixes of a word $a^{j^2}$.
Proving that $L$ is not CFL is done here.
You can use the pumping lemma for CFL or, even better, the pumping lemma for regular languages (using the fact that a CFL over a one-letter alphabet is a regular language).
