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Number Theory Level 3

Define $$HF(n)$$ as the hyperfactorial function of $$n$$, where $$\displaystyle HF(n) = \prod_{m=1}^n m^m$$.

For what integer $$n$$, is $$HF(n)$$ equal to the number of milliseconds in a day?

Try to solve this without using a calculator.

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