Please solve the programming task below using a self-contained code snippet in a markdown code block.

You are given an array nums that consists of positive integers.
The GCD of a sequence of numbers is defined as the greatest integer that divides all the numbers in the sequence evenly.

For example, the GCD of the sequence [4,6,16] is 2.

A subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.

For example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].

Return the number of different GCDs among all non-empty subsequences of nums.
 
Please complete the following python code precisely:
```python
class Solution:
    def countDifferentSubsequenceGCDs(self, nums: List[int]) -> int:
```