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 $10$:

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

Sources

• Weisstein, Eric W. "Factorion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Factorion.html