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Do you perhaps mean "factorion"? I am not familiar with the term "factorgon."

A factorion is an integer which is equal to the sum of factorials of its digits. There are exactly four such numbers:

1 | = | 1!

2 | = | 2!

145 | = | 1!+4!+5!

40585 | = | 4!+0!+5!+8!+5!

The factorion of an n-digit number cannot exceed n·9!.

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Q: What is a factorgon in math?
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