# 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 365

- 365 is the number of days in a non-leap year
- 365 is the smallest number that can be written as a sum of two or more consecutive squares in more than 1 way: 365 = 10
^{2} + 11^{2} + 12^{2} = 13^{2} + 14^{2}

## Common Properties of 365

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.

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 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.