# 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 3435

- 3435 = 3
^{3} + 4^{4} + 3^{3} + 5^{5}, it is the only non-trivial number that is equal to the sum of its digits raised to themselves (submitted by Dan MacKinnon)

## Common Properties of 3435

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.

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

Guess what odious numbers are.

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.

A number is said to be *square-free* if its prime decomposition contains no repeated factors.