二元方程无穷解

看到这样一个程序题：

Find the no of positive integral solutions for the equations (1/x) + (1/y) = 1/N! (read 1 by n factorial) Print a single integer which is the no of positive integral solutions modulo 1000007.

Input:
N
Output:
Number of positive integral solutions for (x,y) modulo 1000007
Constraints:
1 <= N <= 10^6
Sample Input00:
1

Sample Output00:
1

 

Sample Input01:

32327

Sample Output 01:

656502

Sample Input02:

40921

Sample Output 02:

686720

感觉有点困难，希望有意者可以给出解，感激不尽！