# 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 228

- 228 is the smallest number for which the harmonic mean of its nontrivial unitary divisors is an integer (3, 4, 12, 19, 57, and 76 are nontrivial unitary divisor and their harmonic mean is 8)
- The binary form of 228 contains all the two digit binary strings in sequence from highest to lowest

## Common Properties of 228

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.