牛客网暑期ACM多校训练营(第三场) H Diff-prime Pairs

  • 2018-07-26
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题目:

Eddy has solved lots of problem involving calculating the number of coprime pairs within some range. This problem can be solved with inclusion-exclusion method. Eddy has implemented it lots of times. Someday, when he encounters another coprime pairs problem, he comes up with diff-prime pairs problem. diff-prime pairs problem is that given N, you need to find the number of pairs (i, j), where img and img are both prime and i ,j ≤ N. gcd(i, j) is the greatest common divisor of i and j. Prime is an integer greater than 1 and has only 2 positive divisors.

Eddy tried to solve it with inclusion-exclusion method but failed. Please help Eddy to solve this problem.

Note that pair (i1, j1) and pair (i2, j2) are considered different if i1 ≠ i2 or j1 ≠ j2.

Input:

Input has only one line containing a positive integer N.

1 ≤ N ≤ 107

Output:

Output one line containing a non-negative integer indicating the number of diff-prime pairs (i,j) where i, j ≤ N

Sample Input:

3

Sample Output:

2

Sample Input:

5

Sample Output:

6

题目链接

比赛前期解这道题的时候直接跳过了枚举的想法,以为要推公式,局限在了组合数公式中,后来感觉越推越迷就尝试着写了一下暴力,还真过了,看来有些签到题目该直接上还是要直接上啊。

先用筛法打表素数,直接在2 \rightarrow n中间找到所有素数,通过n/i判断i和另一个素数j(j是否可以同时扩大k倍组成另一组i、j使得imgimg也是一组解,计数加结果。

AC代码:

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