$1 \cdot 46$ A proper divisor of a natural number is a positive integer divisor other than 1 and the number itself. A natural number greater than 1 is called "good" if it equals the product of all its distinct proper divisors. What is the sum of the first 10 "good" natural numbers?
[Solution] Clearly, a "good" natural number is either the product of two prime numbers or the cube of a prime number. Therefore, the sum of the first 10 "good" natural numbers is
$$
\begin{aligned}
& 6+8+10+14+15+21+22+26+27+33 \\
= & 182 .
\end{aligned}
$$