D._Small_GCD题解(codeforces 911 div.2)

题干：

Let $a$, $b$, and $c$ be integers. We define function $f(a,b,c)$ as follows:

Order the numbers $a$, $b$, $c$ in such a way that $a\le b\le c$. Then return $\gcd (a,b)$, where $\gcd (a,b)$ denotes the greatest common divisor (GCD) of integers $a$ and $b$.

So basically, we take the $\gcd$ of the $2$ smaller values and ignore the biggest one.

You are given an array $a$ of $n$ elements. Compute the sum of $f(a_i,a_j,a_k)$ for each $i$, $j$, $k$, such that $1\le i<j<k\le n$.

More formally, compute

$$\sum _{i=1}^n\sum _{j=i+1}^n\sum _{k=j+1}^{n}f(a_i,a_j,a_k).$$

输入要求：

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le 10$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($3\le n\le 8\cdot 10^4$) — length of the array $a$.

The second line of each test case contains $n$ integers, $a_1,a_2,\dots$