IMO 1992 LL ROM64

For any positive integer n consider all representations n =

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IMO 1992 LL ROM64

Origin: ROM

Problem

For any positive integer n consider all representations n = a1 + \cdot \cdot \cdot + ak, where a1 > a2 > \cdot \cdot \cdot > ak > 0 are integers such that for all i \in{1, 2, . . ., k −1}, the number ai is divisible by ai+1. Find the longest such representation of the number 1992.