# 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 404

- 404 is the HTTP status code for "file not found", perhaps the most famous HTTP status code of all
- 405 is the smallest composite number that is the sum of two, three, four, and five consecutive composite numbers (405 = 202 + 203 = 134 + 135 + 136 = 99 + 100 + 102 + 104 = 78 + 80 + 81 + 82 + 84)
- 405 is the smallest number with 10 odd divisors

## Common Properties of 404

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.

One can take the sum of the squares of the digits of a number. Those numbers are *happy* for which iterating this operation eventually leads to 1.

A *palindrome* is a number that reads the same forward or backward.

*Undulating* numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.