Package g3601_3700.s3671_sum_of_beautiful_subsequences

Class Solution

java.lang.Object

g3601_3700.s3671_sum_of_beautiful_subsequences.Solution

public class Solution
extends Object

3671 - Sum of Beautiful Subsequences.

Hard

You are given an integer array nums of length n.

For every positive integer g, we define the beauty of g as the product of g and the number of strictly increasing subsequences of nums whose greatest common divisor (GCD) is exactly g.

Return the sum of beauty values for all positive integers g.

Since the answer could be very large, return it modulo 109 + 7.

Example 1:

Input: nums = [1,2,3]

Output: 10

Explanation:

All strictly increasing subsequences and their GCDs are:

Subsequence	GCD
[1]	1
[2]	2
[3]	3
[1,2]	1
[1,3]	1
[2,3]	1
[1,2,3]	1

Calculating beauty for each GCD:

GCD	Count of subsequences	Beauty (GCD × Count)
1	5	1 × 5 = 5
2	1	2 × 1 = 2
3	1	3 × 1 = 3

Total beauty is 5 + 2 + 3 = 10.

Example 2:

Input: nums = [4,6]

Output: 12

Explanation:

All strictly increasing subsequences and their GCDs are:

Subsequence	GCD
[4]	4
[6]	6
[4,6]	2

Calculating beauty for each GCD:

GCD	Count of subsequences	Beauty (GCD × Count)
2	1	2 × 1 = 2
4	1	4 × 1 = 4
6	1	6 × 1 = 6

Total beauty is 2 + 4 + 6 = 12.

Constraints:

• 1 <= n == nums.length <= 104
• 1 <= nums[i] <= 7 * 104

Constructor Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
int	totalBeauty(int[] nums)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Solution

public Solution()

Method Details

totalBeauty

public int totalBeauty(int[] nums)