# Summing Powers

Number Theory Level 4

For all positive integers $$n\leqslant k$$, there exists $$a_1,a_2,a_3,\ldots,a_n$$ that satisfies the following: $\overline{a_1 a_2 a_3\ldots a_n}=(a_1+a_2+a_3+\ldots+a_n)^n$ Find the greatest value of $$k$$.

(Note: $$a_1,a_2,a_3,\ldots,a_n$$ are digits of $$\overline{a_1a_2a_3\ldots a_n}$$)

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