Leetcode 3671. Sum of Beautiful Subsequences

Compute the sum over all positive g of g times the number of strictly increasing subsequences of nums whose GCD equals g (mod 1e9+7). The algorithmic challenge is to count increasing subsequences while dynamically aggregating their gcds efficiently for up to 10^4 elements and values up to 7·10^4, typically via DP/maps that merge gcd states instead of naive enumeration.