EQUATIONS

Solution:
1/x + 1/y = 1/N!
=> x = y*N!/(y-N!)

Say y = N!+Z,
=> x = (N!+Z)*N! / Z = N!^2 / Z + N!.
For 'x' to be integer, 'Z' can take values equal to the no. of divisors of N!^2.

No .of divisors is calculated in the following manner: http://technocratme.blogspot.in/2012/07/divisor-counting.html

import java.util.Scanner;

public class EQUATIONS {

public static int getPowerOfPrimeInNFact(int N,int prime){
int pow = N/prime;
int tmp = 0;
while(pow>0){
tmp +=pow;
pow = pow/prime;
}
return tmp;
}
public static void main(String args[]) throws Exception {
Scanner in = new Scanner((System.in));
//System.out.println(getPowerOfPrimeInNFact(18,3));
int N = in.nextInt();
boolean isComposite[] = new boolean[1000001];
int [] powPrimes = new int[1000001];
// calculate all primes in first 1 million
for(int i=2;i<=1000;i++){
if(!isComposite[i]){ // if prime
for(int j=i*i;j<=1000000;j+=i){
isComposite[j] = true;
}
}
}
long no_div = 1;
for(int i=2;i<=N;i++){
if(!isComposite[i]){ // if prime
//System.out.println(i);
// Find powers of all primes
powPrimes[i] = getPowerOfPrimeInNFact(N,i);
// find the continual mod of the tot. no. of divisors of N!*N!
no_div = ((2*powPrimes[i]+1)*no_div)%1000007;
}
}
System.out.println(no_div);
}
}