# 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 405

- 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 405

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 *odd* if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

The number n is *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.