# Go forth and multiply

Number Theory Level pending

Let $$n\leq 10^6$$ be a $$k$$ digit positive integer written as $$n=\overline{d_1d_2\cdots d_k}$$.

Let $$n_1,n_2,\cdots,n_p$$ be the $$p$$ solutions for the equation

$n=k^2\prod_{i=1}^{k}d_i$

What is the value of $\sum_{i=1}^{p} n_i$

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