# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 504

- 504 is the smallest number n, such that σ(x) = n has exactly ten solutions, where σ(x) means the sum of the divisors
- 504 is the smallest sum of numbers in an amicable pair
- 504 is the smallest number with two pairs of divisors that multiply to the number itself and are reverses of each other (504 = 42*12 = 24*21)
- 504 is the smallest number such that the digits of σ(n) are a permutation of the digits of σ(n)-n

## Common Properties of 504

The number n is *abundant* if the sum of all its positive divisors except itself is more than n.

They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.

A positive integer greater than 1 that is not prime is called *composite*.

Composite numbers are opposite to prime numbers.

A number is *even* if it is divisible by 2.

Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.

The number n is *evil* if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

The number n is *practical* if all numbers strictly less than n are sums of distinct divisors of n.