Tue, 30 Apr 2013 13:26:00 GMT

Counting fractions

TimeLimit: 2000MS MemoryLimit: 65536 Kb

Totalsubmit: 39 Accepted: 6

Description

Consider the fraction, n/d, where n and d are positive integers. If n <= d and HCF(n,d)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for d <= 8 in ascending order of size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that there are 21 elements in this set.

How many elements would be contained in the set of reduced proper fractions for d <= x?

Input

The input will consist of a series of x, 1 < x < 1000001.

Output

For each input integer x, you should output the number of elements contained in the set of reduced proper fractions for d <= x in one line.

Sample Input

Sample Output

3
21

Hint

HCF代表最大公�U�数

�q�里主要说一�?strong>素数�{�法�Q�该�Ҏ��可以快速的选取�?~N数字中的所有素数。时间复杂度�q�小于O(N*sqrt(N))

�Ҏ��为：�?开始，往后所有素数的倍数都不是素数。最后剩下的数都是素数�?/div>

再说说欧拉公式，用来解决所有小于n中的数字有多��个与n互质�Q�用Ψ(n)表示�?/div>

Ψ(n)=n*(1-1/q1)*(1-1/q2)*……*(1-1/qk),n为和敎ͼ�其中qi为n的质因数�?br />Ψ(n)=n-1�Q�n��?br />

注意�Q�关于数论的题很�Ҏ��过int�c�d��的范��_��多考虑用long long�c�d��?br />�Ƨ拉函数请参阅：http://zh.wikipedia.org/zh-cn/%E6%AC%A7%E6%8B%89%E5%87%BD%E6%95%B0

代码

久久国产亚洲精品麻豆,国产福利电影一区二区三区久久久久成人精品综合 ,久久精品国产久精国产