Factor it Out!

Number Theory Level pending

A number is called "special" when its value is equal to ten times the number of factors it has (all natural number factors). For example, 120 has 12 factors, so it is considered special. How many special numbers are there?

Details and Assumptions:

0 is not a special number.

Challenge: If you think there is a point when there are no more special numbers, prove it.


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