than itself. So the number 26 is deficient because its divisors 1, 2 and 13 add up
to only 16, which is less than 26. Prime numbers are very deficient because the
sum of their divisors is always just 1.
A number that is neither superabundant nor deficient is perfect. The addition
of the divisors of a perfect number equal the number itself. The first perfect
number is 6. Its divisors are 1, 2, 3 and when we add them up, we get 6. The
Pythagoreans were so enchanted with the number 6 and the way its parts fitted
together that they called it ‘marriage, health and beauty’. There is another story
connected with 6 told by St Augustine (354–430). He believed that the perfection
of 6 existed before the world came into existence and that the world was created
in 6 days because the number was perfect.
The next perfect number is 28. Its divisors are 1, 2, 4, 7 and 14 and, when we
add them up, we get 28. These first two perfect numbers, 6 and 28, are rather
special in perfect number lore for it can be proved that every even perfect
number ends in a 6 or a 28. After 28, you have wait until 496 for the next