# 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 magic constant of a 5-by-5 magic cube. By the way, such a cube was discovered only in 2013, and smaller magic cubes, except for the trivial one, do not exist
- 315 is the smallest n such that φ(n-1) + φ(n+1) = σ(n)/2
- 315 is the smallest not squarefree 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