lightoj1370——Bi-shoe and Phi-shoe（欧拉函数应用）-白红宇

lightoj1370——Bi-shoe and Phi-shoe（欧拉函数应用）

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发布时间：2019-05-10

本文共 2047 字，大约阅读时间需要 6 分钟。

Description

Bamboo Pole-vault is a massively popular sport in Xzhiland. And Master Phi-shoe is a very popular coach for his success. He needs some bamboos for his students, so he asked his assistant Bi-Shoe to go to the market and buy them. Plenty of Bamboos of all possible integer lengths (yes!) are available in the market. According to Xzhila tradition,

Score of a bamboo = Φ (bamboo’s length)

(Xzhilans are really fond of number theory). For your information, Φ (n) = numbers less than n which are relatively prime (having no common divisor other than 1) to n. So, score of a bamboo of length 9 is 6 as 1, 2, 4, 5, 7, 8 are relatively prime to 9.

The assistant Bi-shoe has to buy one bamboo for each student. As a twist, each pole-vault student of Phi-shoe has a lucky number. Bi-shoe wants to buy bamboos such that each of them gets a bamboo with a score greater than or equal to his/her lucky number. Bi-shoe wants to minimize the total amount of money spent for buying the bamboos. One unit of bamboo costs 1 Xukha. Help him.

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 10000) denoting the number of students of Phi-shoe. The next line contains n space separated integers denoting the lucky numbers for the students. Each lucky number will lie in the range [1, 106].

Output

For each case, print the case number and the minimum possible money spent for buying the bamboos. See the samples for details.

Sample Input

1 2 3 4 5

10 11 12 13 14 15

1 1

Sample Output

Case 1: 22 Xukha

Case 2: 88 Xukha

Case 3: 4 Xukha

每个人有一个幸运值n，求欧拉函数Φ(x)>=n的最小的那个x。

根据欧拉函数的定义，素数n的欧拉函数值一定是n-1，所以在两个素数的区间(n1,n2)中的数（这肯定是合数）的欧拉函数值肯定小于Φ(n2)。所以给定一个数x，距这个数x+1的最近的素数就是要求的数，因为x+1以下的数的欧拉函数值肯定不会超过x。

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        #include 
        
         #include 
         #include 
          
           #include 
           
            #define INF 0x3f3f3f3f#define MAXN 1000005#define mod 1000000007using namespace std;int p[MAXN];void Init(){ for(int i=2; i

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