数学hdu5072

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Coprime Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others) Total Submission(s): 109    Accepted Submission(s): 51 Problem Description There are n people standing in a line. Each of them has a unique id number. Now the Ragnarok is coming. We should choose 3 people to defend the evil. As a group, the 3 people should be able to communicate. They are able to communicate if and only if their id numbers are pairwise coprime or pairwise not coprime. In other words, if their id numbers are a, b, c, then they can communicate if and only if [(a, b) = (b, c) = (a, c) = 1] or [(a, b) ≠ 1 and (a, c) ≠ 1 and (b, c) ≠ 1], where (x, y) denotes the greatest common divisor of x and y. We want to know how many 3-people-groups can be chosen from the n people.   Input The first line contains an integer T (T ≤ 5), denoting the number of the test cases. For each test case, the first line contains an integer n(3 ≤ n ≤ 10 5), denoting the number of people. The next line contains n distinct integers a 1, a 2, . . . , a n(1 ≤ a i  ≤ 10 5) separated by a single space, where a i  stands for the id number of the i-th person.   Output For each test case, output the answer in a line.   Sample Input 1 5 1 3 9 10 2   Sample Output 4   Source 2014 Asia AnShan Regional Contest

鞍山现场赛的题，当时没做出来，现在补上

题意：告诉你n个数问有多少个三元组(a,b,c)，满足要么两两互质，要么两两不互质

思路：设这三个数为a,b,c，现在假设a与b互质，b与c不互质，设满足这样的集合数位temp,那么答案为C(n,3)-temp/2，之所以除2是因为b作为中间的数算重了一次。 现在问题转为求解temp。  对于每个b，设与它互质的数个数为cnt1,与它不互质的个数为cnt2，显然cnt1+cnt2+1=n。 那么对于b的temp值为cnt1*cnt2，其中只需要求出cnt2即可，将b分解质因子，然后这些质因子的个数不会超过6个，显然可以状压以后容斥原理求解。 现在问题进而转化为求出一个数x有多少个数是x的倍数，这个用素数筛选可以求得，问题得以解决。

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