Longest Divisible Subsequence

For a given numeric sequence a_1, a_2, \ldots, a_n, find the length of the maximum divisible subsequence.

A divisible subsequence a_{k_1}, a_{k_2}, \ldots, a_{k_t} (k_1 < k_2 < \ldots < k_t) is one where a_{k_i} \mid a_{k_j} holds for 1 \leq i < j \leq t (the statement "a \mid b" is equivalent to "$b$ is divisible by $a$"). A subsequence consisting of a single element is considered divisible by definition.