Let dp[k][cur] be the number of good sequences with k numbers that ends with cur. So —

Recurrence : From a number cur we can move to all the divisors of cur. Say the divisors of cur are — x1, x2, x3, ... xn. Then our recurrence will look like —

dp[n][cur] = dp[n-1][x1] + dp[n-1][x2] + ... dp[n-1][xn]

Base case : It's easy to tell that base case is for n = 1. (Figure out what you have to do then)

Now you only need to find a good way to store all the divisors of the numbers from 1 to 2000.

You can see my code if you get stuck : 27958781