Problem 34

Digit factorials

$145$ is a curious number, as $1! + 4! + 5! = 1 + 24 + 120 = 145$.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: as $1! = 1$ and $2! = 2$ are not sums they are not included.

$145$是个有趣的数，因为$1! + 4! + 5! = 1 + 24 + 120 = 145$。

找出所有各位数字的阶乘和等于其本身的数，并求它们的和。

注意：因为$1! = 1$和$2! = 2$不是和的形式，所以它们并不在讨论范围内。