# 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 288

- 288 is the number of completed Sudokus of size 4 by 4
- 288 is the smallest non-palindrome non-square without trailing zeros such that when multiplied by its reverse is a square: 288 * 882 = 504
^{2}
- 288 = 1
^{1} + 2^{2} + 3^{3} + 4^{4}
- 288 is the product of the first four factorials
- 288 is the smallest number that is a member of an amicable pair where only abundant aliquot parts are considered: (288 is paired with 450)

## Common Properties of 288

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.