# TotallyOriginallyCreatedByMe Number

Let $$\overline{a_1 a_2 a_3 \ldots a_n}$$ be the smallest $$n$$-digit number greater than $$1$$ with $$a_1, a_2, a_3, \ldots, a_n \ne 0$$ such that $$\large \displaystyle \sum_{k=1}^n a_k^{a_k} = \overline{a_1 a_2 a_3 \ldots a_n}$$. What is the value of $$\displaystyle \prod_{k=1}^n a_k$$?

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