# 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 216

- 216 is the smallest untouchable number which is also a cube
- Plato's number: Plato alludes to the fact that 216 is equal to 6
^{3}, where 6 is one of the numbers representing marriage since it is the product of the female 2 and the male 3. Plato was also aware of the fact the the sum of the cubes of the 3-4-5 Pythagorean triple is equal to 216
- 216 = 2
^{3}*3^{3} = 6^{3} = 3^{3} + 4^{3} + 5^{3}, making it the smallest cube that's also the sum of three cubes
- 216 is the the number of colors in the Netscape Web-safe color palette
- 216 is the smallest magic product of a 3 by 3 multiplicative magic square
- 216 is the smallest abundant cube
- 216 is the smallest number with more abundant divisors than deficient divisors
- 216 is the smallest volume of an integer-sized brick that has the same surface area as volume

## Rare Properties of 216

The number n is a *cube* if it is the cube of an integer.

## Common Properties of 216

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.

An integer n is *powerful* if for every prime p dividing n, p^{2} also divides n.

How much power? They all can be written as a^{2} b^{3}.

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

The *untouchable* numbers are those that are not the sum of the proper divisors of any number.