# Definition:Factorion

## Definition

A factorion (base $b$) is a positive integer which, when expressed in base $b$, equals the sum of the factorials of its digits.

When the number base is not given, base $10$ is assumed.

## Examples

### Factorions Base $10$

The following positive integers are the only factorions base $10$:

$1, 2, 145, 40 \, 585$