# 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 220

- 220 is the smallest amicable number
- The diagonals of a regular decagon divide it into 220 regions

## Rare Properties of 220

The number n is *amicable* if it belongs to an amicable pair. Two numbers n and m are called an *amicable pair* if the sum of all positive divisors of n is equal to the sum of all positive divisors of m and both are equal to n + m.

It all started with perfect numbers which are amicable with themselves. Those numbers adopted social virtues and qualities; for the parts of each of them have the power to generate the other. See also sociable numbers.

A *tetrahedral* number is the number of balls you can put in a triangular pyramid.

This is the space generalization of triangular and square numbers.

## Common Properties of 220

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.

The number n is called an *apocalyptic power* if 2^{n} contains the consecutive digits 666 (in decimal).

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 *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

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