For positive integer $n$ such that $n < 10{,}000$, the number $n+2005$ has exactly 21 positive factors. What is the sum of all the possible values of $n$?
Question:
For positive integer $n$ such that $n < 10{,}000$, the number $n+2005$ has exactly 21 positive factors. What is the sum of all the possible values of $n$?
Answer:
Let's think step by step.

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For positive integer $n$ such that $n < 10{,}000$, the number $n+2005$ has exactly 21 positive factors. What is the sum of all the possible values of $n$?
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