Number of Different Subsequences GCDs
We need to find the number of different GCDs (Greatest Common Divisors) among all nonempty subsequences of the given array nums
.
The idea here is to notice that there is no need to check all possible subsequences directly. Instead, we can leverage the mathematical properties of GCD to find the answer in an efficient manner.
Here’s a stepbystep approach:
 Find the Maximum Element: Determine the maximum element
max_num
in the arraynums
.  Create a Frequency Table: Make a frequency table that counts the number of occurrences of each integer from
1
tomax_num
.  Check Possible GCDs: Iterate from
max_num
down to1
and check if each integer can be a GCD of some subsequence. Use the frequency table to check this by considering the multiples of each integer.  Count Different GCDs: Count the number of different GCDs found in step 3.
Here’s the code:


The solution efficiently iterates through the possible GCDs, leveraging the mathematical properties of GCD, and checks if each one can be the GCD of some subsequence. It returns the count of different GCDs among all nonempty subsequences of nums
.