Find all positive integers $latex n$ that have distinct positive divisors $latex d_1$, $latex d_2$,$latex \ldots$, $latex d_k$, where $latex k > 1$, that are in arithmetic progression and

$latex n=d_1 +d_2 + \cdots +d_k.$

Note that $latex d_1$, $latex \ldots$, $latex d_k$ do not need to be all the divisors of $latex n$.

Due day is March 29.