# 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 240

- 240 is the smallest number with 20 divisors
- The maximum number of divisors for any integer less than a million is 240
- 240 is the smallest magic constant of a pan-diagonal magic square which consist of distinct prime numbers (this square is of order 4)
- The most special root system E
_{8} has 240 root vectors
- 240 is the largest side of the smallest Euler brick
- Soma cube has 240 solutions
- There 240 mountain numbers (digits go up then down) with 3 digits

## Rare Properties of 240

The number is called *pronic* if it is the product of two consecutive numbers.

They are twice triangular numbers.

## Common Properties of 240

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.