# 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 315

- 315 is the smallest n such that φ(n-1) + φ(n+1) = σ(n)/2
- 315 is the smallest squareful order of a cyclotomic polynomial containing a coefficient with an absolute value greater than one
- 315 is the smallest odd number such that its sum of divisors is larger than the sums of divisors of its neighbors

## Common Properties of 315

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.