# Summing Powers

For all positive integers $$1<n\leqslant k$$, there exist non-negative single digit integers $$a_1,a_2,a_3,\ldots,a_n$$ $$(a_1\ne 0)$$ which satisfy $\overline{a_1a_2a_3\ldots a_n}=( a_1+ a_2+ a_3+\cdots+ a_n)^n.$

Find the greatest value of $$k$$.

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