Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		int[] array = new int[n + 1];

		for(int i = 2; i <= n; i++) {//2~nに対して
			int a = i;
			for(int j = 2; j <= a;) {//素因数分解して、因数をarray配列に詰める
				if(a % j == 0) {
					a = a / j;
					array[j]++;
				} else {
					j++;
				}
			}
		}
		long sum = 1;
		for(int i = 0; i <= n; i++) {
			sum *= (array[i] + 1);
			sum %= 1000000007;
		}

		System.out.println(sum);
	}
}