Minimum’s Revenge HDU5922 （水t）

Minimum’s Revenge

Problem Description

There is a graph of n vertices which are indexed from 1 to n. For any pair of different vertices, the weight of the edge between them is the least common multiple of their indexes.

Mr. Frog is wondering about the total weight of the minimum spanning tree. Can you help him?

 

Input

The first line contains only one integer T (T≤100), which indicates the number of test cases.

For each test case, the first line contains only one integer n (2≤n≤109), indicating the number of vertices.

 

Output

For each test case, output one line "Case #x：y",where x is the case number (starting from 1) and y is the total weight of the minimum spanning tree.

 

Sample Input

223

 

Sample Output

Case #1: 2Case #2: 5
Hint
In the second sample, the graph contains 3 edges which are (1, 2, 2), (1, 3, 3) and (2, 3, 6). Thus the answer is 5.
 

 

Source

2016CCPC东北地区大学生程序设计竞赛 - 重现赛

 

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wange2014

边界问题 除以2问题  害我2wa T_T T_T 太粗心

求一个最小生成树   且权值就是两点连线的gcd

那么 直接与1相连的gcd会最小

即输出2+3+......+n

公式 (n-1)*(2+n)/2;

直接输出会越int界

所以变形  且不要出现/2有小数问题

得出 ans = n*(n-1)/2+n-1

代码略