# 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 345

- 345 is the smallest number that is a concatenation of the sides of a Pythagorean triangle
- 345 is the smallest number for which the harmonic mean of nontrivial divisors is an integer and which is not a prime square
- 345 is the smallest number such that its largest nontrivial divisor equals the sum of its the other nontrivial divisors (The nontrivial divisors of 345 are 3, 5, 15, 23, 69, 115, the largest of which, 115, is equal to the sum of the other nontrivial divisors)
- 345 is the smallest number that can be written as a concatenation of twin primes and their average