# 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 1210

- 1210 is the smallest autobiographical number: n = x
_{0}x_{1}x_{2}...x_{9} such that x_{i} is the number of digits equal to i in n: 1210 is built of one 0, two 1s, and one 2

## Rare Properties of 1210

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.

## Common Properties of 1210

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

Composite numbers are opposite to prime numbers.

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

Compare with perfect and abundant 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.