#1819
Number of Different Subsequences GCDs
hard · verified · 45.1% accepted · 436 likes · top 28%
array · math · counting · number theory
Description
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.
Example 1:
Input: nums = [6,10,3]
Output: 5
Explanation: The figure shows all the non-empty subsequences and their GCDs.
The different GCDs are 6, 10, 3, 2, and 1.
Example 2:
Input: nums = [5,15,40,5,6]
Output: 7
Solution