CF1575G GCD Festival

Mr. Chanek has an array $ a $ of $ n $ integers. The prettiness value of $ a $ is denoted as: $ $$$\sum_{i=1}^{n} {\sum_{j=1}^{n} {\gcd(a_i, a_j) \cdot \gcd(i, j)}} $ $

where $ \\gcd(x, y) $ denotes the greatest common divisor (GCD) of integers $ x $ and $ y $ .

In other words, the prettiness value of an array $ a $ is the total sum of $ \\gcd(a\_i, a\_j) \\cdot \\gcd(i, j) $ for all pairs $ (i, j) $ .

Help Mr. Chanek find the prettiness value of $ a $ , and output the result modulo $ 10^9 + 7$$$!

The first line contains an integer $ n $ ( $ 2 \leq n \leq 10^5 $ ). The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 10^5 $ ).

Output an integer denoting the prettiness value of $ a $ modulo $ 10^9 + 7 $ .