Am I missing a trick with perfect numbers?
The investigation of perfect numbers dates back to the ancient Egyptians. It is believed that they were interested in perfect numbers in part because of a superstitious numerology which was important in their culture, but also because of the limits and conventions of their mathematical notation. They could write down fractions only like 1/2, 1/3, 1/4, 1/5, etc., that is, fractions that we write with numerator = 1 and denominator = some integer, and they recorded all other fractions as sums of these special fractions. Also they did not use any of their fractions more than once in any one of these sums (I don’t know the reason for this). Thus, 3/7 would never be “1/7 + 1/7 + 1/7”; it would be “1/3 + 1/11 + 1/231” or maybe “1/4 + 1/6 + 1/84”. They noticed that, for some numbers (the perfect numbers), the sum of all the Egyptian fractions with denominators greater than 1 which are divisors of the numbers is always equal to one. So for the perfect number 6, 1/2 + 1/3 + 1/6 = 1. For 28, 1/2
