A14495 | GCD Festival

Mr. Chanek has an array $a$ of $n$ integers. The prettiness value of $a$ is denoted as:

$$$$\sum_{i=1}^{n} {\sum_{j=1}^{n} {\gcd(a_i, a_j) \cdot \gcd(i, j)}} $$ </p><p>where $\\gcd(x, y)$ denotes the greatest common divisor (GCD) of integers $x$ and $y$ .</p><p>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 $(i, j)$ .</p><p>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 $10^9 + 7$ .