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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