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Problem 34

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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.

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数字阶乘和

$145$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。

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