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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;

class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }
    static void Solve()
    {
        var N = sc.ReadInt();
        var era = new SieveOfEratosthenes(N);
        var count = new int[N + 1];
        for (int x = 1; x <= N; x++)
        {
            var pf = era.PrimeFactorsTup(x);
            foreach (var t in pf)
            {
                count[t.Item1] += t.Item2;
            }
        }

        var ans = 1L;
        for (int i = 0; i < N+1; i++)
        {
            ans *= count[i] + 1;
            ans %= (long)1e9 + 7;
        }
        Console.WriteLine(ans);
    }

    class SieveOfEratosthenes
    {
        public int[] Table;
        public SieveOfEratosthenes(int max)
        {
            CreateTable(max);
        }
        // n以下の数について、最小素因数を記録した表を生成する
        private void CreateTable(int n)
        {
            Table = Enumerable.Range(0, n + 1).ToArray();
            if (n <= 3) return;
            // 2の倍数の最小素因数は2
            for (int i = 2; i <= n; i += 2) Table[i] = 2;
            // 3以上の奇数について最小素因数を記録する
            for (int p = 3; p * p <= n; p += 2)
            {
                // 奇数pがp未満の数の倍数である場合は無視
                if (Table[p] < p) continue;
                // 素数pの倍数を記録
                for (int x = p; x <= n; x += p)
                {
                    Table[x] = p;
                }
            }
        }
        // 最小素因数表を使って素因数分解を行う
        public List<int> PrimeFactors(int n)
        {
            var res = new List<int>();
            while (Table[n] != 1)
            {
                res.Add(Table[n]);
                n /= Table[n];
            }
            return res;
        }
        // 素因数を(p, 個数)のペアで返す
        public List<Tuple<int, int>> PrimeFactorsTup(int n)
        {
            var prev = 0;
            var count = 0;
            var res = new List<Tuple<int, int>>();
            if (n <= 1) return res;
            foreach (var p in PrimeFactors(n))
            {
                if (prev != p)
                {
                    if (count > 0) res.Add(Tuple.Create(prev, count));
                    count = 1;
                }
                else count++;
                prev = p;
            }
            res.Add(Tuple.Create(prev, count));
            return res;
        }
        // 素数判定
        public bool IsPrime(int n)
        {
            return Table[n] == n;
        }
    }
    static Scanner sc = new Scanner();
}
class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public Tuple<int, int> ReadTup(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<long, long> ReadTupLong(int add = 0)
    {
        return Tuple.Create(this.ReadLong() + add, this.ReadLong() + add);
    }
    public Tuple<int, int, int> ReadTup3(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<int, int, int, int> ReadTup4(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
    public Tuple<long, long>[] ReadTupLongArray(int n, int add = 0)
    {
        var array = new Tuple<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTupLong(add);
        }
        return array;
    }
    public Tuple<int, int>[] ReadTupArray(int n, int add = 0)
    {
        var array = new Tuple<int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup(add);
        }
        return array;
    }
    public Tuple<int, int, int>[] ReadTup3Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup3(add);
        }
        return array;
    }
    public Tuple<int, int, int, int>[] ReadTup4Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup4(add);
        }
        return array;
    }
}