GCD Festival

题意翻译

给定长度为 $n$ 的正整数数组 $a_1,...,a_n$。计算 $$ \sum_{i=1}^n\sum_{j=1}^n \gcd(a_i,a_j)\times \gcd(i,j) $$ 答案对 $10^9+7$ 取模。保证 $1\leq n,a_i\leq 10^5$。

题目描述

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$!

输入输出格式

输入格式

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 $ ).

输出格式

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

输入输出样例

输入样例 #1

5
3 6 2 1 4

输出样例 #1

77