LightOJ 1236 Pairs Forming LCM

• 2018-08-08
• 34
• 0

题目:

Find the result of the following code:

A straight forward implementation of the code may time out. If you analyze the code, you will find that the code actually counts the number of pairs (i, j) for which lcm(i, j) = n and (i ≤ j).

Input:

Input starts with an integer T (≤ 200), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 10^{14}).

Output:

For each case, print the case number and the value returned by the function ‘pairsFormLCM(n)’.

15
2
3
4
6
8
10
12
15
18
20
21
24
25
27
29

Sample Output:

Case 1: 2
Case 2: 2
Case 3: 3
Case 4: 5
Case 5: 4
Case 6: 5
Case 7: 8
Case 8: 5
Case 9: 8
Case 10: 8
Case 11: 5
Case 12: 11
Case 13: 3
Case 14: 4
Case 15: 2

题目链接

N=p_{1}^{e_{1}}\times p_{2}^{e_{2}}\times …\times p_{k}^{e_{k}}

i=p_{1}^{i_{1}}\times p_{2}^{i_{2}}\times …\times p_{k}^{i_{k}}

j=p_{1}^{j_{1}}\times p_{2}^{j_{2}}\times …\times p_{k}^{j_{k}}

\because LCM(i,j)=N

\therefore i_{x}<=e_{x},j_{x}=e_{x}i_{x}=e_{x},j_{x}<=e_{x}