poj3090

maksyuki 发表于 oj 分类,标签:
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Visible Lattice Points

A lattice point (xy) in the first quadrant (x and y are integers greater than or equal to 0), other than the origin, is visible from the origin if the line from (0, 0) to (xy) does not pass through any other lattice point. For example, the point (4, 2) is not visible since the line from the origin passes through (2, 1). The figure below shows the points (xy) with 0 ≤ xy ≤ 5 with lines from the origin to the visible points. Write a program which, given a value for the size, N, computes the number of visible points (xy) with 0 ≤ xy ≤ N.

Input

The first line of input contains a single integer C (1 ≤ C ≤ 1000) which is the number of datasets that follow.

Each dataset consists of a single line of input containing a single integer N (1 ≤ N ≤ 1000), which is the size.

Output

For each dataset, there is to be one line of output consisting of: the dataset number starting at 1, a single space, the size, a single space and the number of visible points for that size.

Sample Input

4

2

4

5

231

Sample Output

1 2 5
2 4 13
3 5 21
4 231 32549

Source

Greater New York 2006

 

题目类型:法雷级数

算法分析:所有可见的点的坐标(x, y)满足gcd (x, y) = 1,本题的坐标关系恰好可以使用法雷级数来表示,由于坐标位置存在顺序,所以总的个数等于2倍的F(n)再减去多算的对角线上的一个坐标