A number $n$ is called *insipid* if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.

**Question**: Are there infinitely many insipid numbers?

Let $\iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:

**Bonus question**: Is it true that $\lim_{r \to \infty}r/\iota(r)=2$?