Source: Adapted from *Mathematics Magazine*, 1954, pp. 37-38.

**Hint:** Can the integer N be prime?

Try some numbers with multiple factors...being systematic may or may not help.

**Solution Commentary:** For N (and its divisors d_{n}), we need Σ1/d_{n} = 2. Suppose we multiplied the left expression by N, getting Σ N/d_{n} = Σ d_{n}. Think about why this works…try some examples. But this means that Σ d_{n} = 2N. Surprise….this means N is a perfect number (i.e. a number that is the sum of its proper divisors). Thus, the three smallest perfect numbers are 6, 28, and 496.