Yeah I noticed this, but was too tired to correct it. =)

Anyway my guess was wrong (9!+8!+7!+...) you got it right.

> (way faster than my brute force approach).

If it's about speed you can limit the $maxlevel, because the longest number can't have more than 7 digits:

1. Evidently 0 is excluded!

2. Any number this long includes even ciphers. So 5 is excluded! But any number divisible by 5 and 2 must end with a 0

3. An number from the remaining 8 digits would include 9 and 3, but the digit sum would be 40, which is impossible.¹

Even your approach with a brute force loop could compete when only considering 7 digits, cause you don't have the overhead of 1 million function calls.

¹) and therefor a 7 digit number excludes 4 to be divisible by 9.