MathDB

For any positive integer

n

consider all representations

n = a_1 + \cdots+ a_k

, where

a_1 > a_2 > \cdots > a_k > 0

are integers such that for all

i \in \{1, 2, \cdots , k - 1\}

, the number

a_i

is divisible by

a_{i+1}

. Find the longest such representation of the number

1992.

64