problem: By a proper divisor of a natural number we mean a positive integral divisor other than 1 and the number itself. A natural number greater than 1 will be called "nice" if it is equal to the product of its distinct proper divisors. What is the sum of the first ten nice numbers? solution: We ask the natural "when is an integer $n$ 'nice'?" Note that every integer $n$ comes in positive divisor pairs, $d$ and $n/d$. So, an integer is nice if it only has one other pair of positive divisors aside from $1$ and itself. If a number is a product of two distinct primes, it is therefore nice. We note that squares of primes are not nice since there are just two copies of the same positive proper divisor. Are there any other cases when an integer is nice? Indeed, if we consider cubes of primes, these are nice since the only proper divisors are $p$ and $p^2$. Thus, our answer is $2 \cdot3+2^3+2\cdot5 +3\cdot 5 + 3^3 +2 \cdot 7+ ... = 182$