A factorion equals the sum of the factorials of its own digits. The complete base-10 list is just four numbers: 1, 2, 145 (= 1! + 4! + 5! = 1 + 24 + 120), and 40585 (= 4! + 0! + 5! + 8! + 5!).
The list is provably finite and short: a \(d\)-digit number is at least \(10^{d-1}\), but the digit-factorial sum is at most \(d \times 9! = 362880d\), which can't keep up once \(d \ge 8\). So no factorion can have more than seven digits, and an exhaustive search finds only these four. The term was coined by Clifford Pickover.