Some positive integers have exactly four positive factors. For example, 35 has only 1, 5, 7 and 35 as its factors. What is the sum of the smallest five positive integers that each have exactly four positive factors?
If they have four factors they can be of the form $p_1\cdot p_2$ or $p^3$ for all $p_1,p_2,p$ prime.
Let's do $p_1\cdot p_2$ first. We have $2\cdot 3=6, 2\cdot 5=10, 2\cdot 7=14, 2\cdot 11=22, $ etc. if $2$ is the first. Otherwise we can have $3\cdot 5=15, 3\cdot 7=21$, etc. So the smallest $5$ are $6,10,14,15,21$.
Then for $p^3$ we can have $2^3=8$ and the rest are larger than $21$.
So the numbers are $6,8,10,14,15$. Sum them up.