Problem:
Score : 700 points

Problem Statement

We have N gemstones labeled 1 through N.

You can perform the following operation any number of times (possibly zero).

Select a positive integer x, and smash all the gems labeled with multiples of x.

Then, for each i, if the gem labeled i remains without getting smashed, you will receive a_i yen (the currency of Japan).
However, a_i may be negative, in which case you will be charged money.

By optimally performing the operation, how much yen can you earn?

Constraints

All input values are integers.

1 \leq N \leq 100

|a_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the maximum amount of money that can be earned.

Sample Input 1

6
1 2 -6 4 5 3

Sample Output 1

12

It is optimal to smash Gem 3 and 6.

Sample Input 2

6
100 -100 -100 -100 100 -100

Sample Output 2

200

Sample Input 3

5
-1 -2 -3 -4 -5

Sample Output 3

0

It is optimal to smash all the gems.

Sample Input 4

2
-1000 100000

Sample Output 4

99000

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

class Scanner
{
    private string[] Line;
    private int Index;

    public Scanner()
    {
        Line = new string[0];
        Index = 0;
    }

    public string Next()
    {
        if (Index >= Line.Length)
        {
            Line = Console.ReadLine().Split(' ');
            Index = 0;
        }
        var ret = Line[Index];
        Index++;
        return ret;

    }

    public int NextInt()
    {
        return int.Parse(Next());
    }
}

class Program
{
    private int N;
    private int[] A;

    private void Scan()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        A = new int[N + 1];
        for (int i = 1; i <= N; i++)
        {
            A[i] = sc.NextInt();
        }

    }

    private long Calc(bool[]b)
    {
        var res = 0L;
        for (int i = 1; i <= N; i++)
        {
            if (!b[i])
            {
                res += A[i];
            }
        }
        return res;
    }

    public void Solve()
    {
        Scan();
        bool[] br = new bool[N + 1];
        for (int i = N / 2 + 1; i <= N; i++)
        {
            if (A[i] < 0)
            {
                br[i] = true;
            }
        }
        long ans = Calc(br);
        for (int i = N / 2; i >= 1; i--)
        {
            if (A[i] < 0 && !br[i])
            {
                for (int j = 1; j <= i; j++)
                {
                    if (i % j == 0)
                    {
                        var ar = br.ToArray();
                        for (int k = j; k <= N; k += j)
                        {
                            ar[k] = true;   
                        }
                        var c = Calc(ar);
                        if (ans < c)
                        {
                            ans = c;
                            br = ar;
                        }
                    }
                }
            }
        }
        Console.WriteLine(ans);
    }

    static public void Main()
    {
        new Program().Solve();
    }
}