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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pi = Pair<int, int>;
using PL = Pair<long, int>;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    public static bool chmin<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == 1) { num = val; return true; } return false; }
    public static bool chmax<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == -1) { num = val; return true; } return false; }
    public static void swap<T>(ref T v1, ref T v2)
    { var t = v2; v2 = v1; v1 = t; }
    public static void Fail() => Fail("No");
    public static void Fail<T>(T s) { WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        var p = new Program();
        for (var i = 1; i > 0; --i)
            p.Solve();
        Console.Out.Flush();
    }
    void Solve()
    {
        var num = Input.num;
        var ar = Input.ar;
        var f = new CompLib.Graph.Flow.MaxFlow(num + 2);
        for (var i = 0; i < num; i++)
            if (ar[i] <= 0)
                f.AddDirectedEdge(num, i, -ar[i]);
            else f.AddDirectedEdge(i, num + 1, ar[i]);
        for (var i = 1; i <= num; i++)
            for (var j = i<<1; j <= num; j+=i)
                    f.AddDirectedEdge(i-1, j-1, long.MaxValue);
        WriteLine(ar.Select(a=>(long)a).Where(a => a > 0).Sum() - f.Execute(num,num+1));
    }
}

namespace CompLib.Graph.Flow
{
    using C = System.Int64;
    #region Max Flow
    /// <summary>
    /// 辺の追加を行い，最大流を求めることが可能なグラフです．
    /// </summary>
    public class MaxFlow
    {
        readonly List<Edge>[] G;
        readonly int[] lv, iter;
        /// <summary>
        /// 頂点数 <paramref name="V"/> で辺が存在しないグラフを構築します．
        /// </summary>
        /// <param name="V">頂点の数</param>
        /// <remarks>この操作は O(<paramref name="V"/>) で実行されます．</remarks>
        public MaxFlow(int V)
        {
            G = new List<Edge>[V];
            lv = new int[V];
            iter = new int[V];
            for (int i = 0; i < G.Length; i++)
                G[i] = new List<Edge>();
        }

        /// <summary>
        /// 頂点 <paramref name="from"/> から頂点 <paramref name="to"/> への容量 <paramref name="cap"/> の有向辺を追加します．
        /// </summary>
        /// <param name="from">始点となる頂点の 0-indexed での番号</param>
        /// <param name="to">終点となる頂点の 0-indexed での番号</param>
        /// <param name="cap">辺の容量</param>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public void AddDirectedEdge(int from, int to, C cap)
        {
            addEdge(from, to, cap, 0);
        }

        /// <summary>
        /// 頂点 <paramref name="from"/> から頂点 <paramref name="to"/> への容量 <paramref name="cap"/> の無向辺を追加します．
        /// </summary>
        /// <param name="from">始点となる頂点の 0-indexed での番号</param>
        /// <param name="to">終点となる頂点の 0-indexed での番号</param>
        /// <param name="cap">辺の容量</param>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public void AddUndirectedEdge(int from, int to, C cap)
        {
            addEdge(from, to, cap, cap);
        }
        void addEdge(int f, int t, C c1, C c2)
        {
            var a = new Edge(t, c1);
            var b = new Edge(f, c2);
            Edge.Link(a, b);
            G[f].Add(a);
            G[t].Add(b);
        }


        /// <summary>
        /// 頂点 <paramref name="src"/> から頂点 <paramref name="sink"/> へ最大で流量 <paramref name="f"/> だけフローを流します．
        /// </summary>
        /// <param name="src">ソースとなる頂点の 0-indexed での番号</param>
        /// <param name="sink">シンクとなる頂点の 0-indexed での番号</param>
        /// <param name="f">ソースからシンクへと流す最大の容量．-1を指定した場合，最大流を求める．</param>
        /// <remarks>この操作はDinic法に基づき，最悪計算量 O(EV^2) で実行されます．Vは頂点の数，Eは辺の数ｗ表します．</remarks>
        public C Execute(int src, int sink, C f = -1)
        {
            C flow = 0;
            if (f < 0) f = C.MaxValue;
            while (f > 0)
            {
                bfs(src);
                if (lv[sink] == 0) return flow;
                Array.Clear(iter, 0, iter.Length);
                C df;
                while ((df = dfs(src, sink, f)) > 0) { flow += df; f -= df; }
            }
            return flow;
        }

        void bfs(int s)
        {
            Array.Clear(lv, 0, lv.Length);
            var q = new Queue<int>();
            lv[s] = 1;
            q.Enqueue(s);
            while (q.Count > 0)
            {
                var v = q.Dequeue();
                foreach (var e in G[v])
                    if (e.Cap > 0 && lv[e.To] == 0)
                    {
                        lv[e.To] = lv[v] + 1;
                        q.Enqueue(e.To);
                    }
            }

        }
        C dfs(int v, int t, C f)
        {
            if (v == t) return f;
            C ret = 0;
            for (; iter[v] < G[v].Count; iter[v]++)
            {
                var e = G[v][iter[v]];
                if (e.Cap <= 0 || lv[v] >= lv[e.To]) continue;
                C df = dfs(e.To, t, Math.Min(f, e.Cap));
                if (df <= 0) continue;
                e.Cap -= df;
                e.Rev.Cap += df;
                ret += df; f -= df;
                if (f == 0) break;
            }
            return ret;

        }
        class Edge
        {
            public static void Link(Edge e1, Edge e2)
            {
                e1.Rev = e2; e2.Rev = e1;
            }
            public int To { get; private set; }
            public Edge Rev { get; private set; }
            public C Cap { get; set; }
            public Edge(int t, C c)
            {
                To = t;
                Cap = c;
            }
            public override string ToString()
            {
                return string.Format("to: {0}, cap: {1}", To, Cap);
            }
        }


    }
    #endregion
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static T[] Create<T>(int n, Func<T> f)
        => Enumerable.Repeat(0, n).Select(_ => f()).ToArray();
    public static char[][] grid(int h)
        => Create(h, () => read.ToCharArray());
    public static int[] ar1D(int n)
        => Create(n, () => num);
    public static long[] arL1D(int n)
        => Create(n, () => numL);
    public static string[] strs(int n)
        => Create(n, () => read);
    public static int[][] ar2D(int n)
        => Create(n, () => ar);
    public static long[][] arL2D(int n)
        => Create(n, () => arL);
    public static List<T>[] edge<T>(int n)
        => Create(n, () => new List<T>());
    public static void Make<T1, T2>(out T1 v1, out T2 v2)
    {
        v1 = Next<T1>();
        v2 = Next<T2>();
    }
    public static void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        Make(out v1, out v2);
        v3 = Next<T3>();
    }
    public static void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        Make(out v1, out v2, out v3);
        v4 = Next<T4>();
    }
    public static void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        Make(out v1, out v2, out v3, out v4);
        v5 = Next<T5>();
    }
    public static void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6)
    {
        Make(out v1, out v2, out v3, out v4, out v5);
        v6 = Next<T6>();
    }
    static Input()
    {
        sc = new Queue<string>();
        dic = new Dictionary<Type, Func<string, object>>();
        dic[typeof(int)] = s => int.Parse(s);
        dic[typeof(long)] = s => long.Parse(s);
        dic[typeof(char)] = s => char.Parse(s);
        dic[typeof(double)] = s => double.Parse(s);
        dic[typeof(uint)] = s => uint.Parse(s);
        dic[typeof(ulong)] = s => ulong.Parse(s);
        dic[typeof(string)] = s => s;
    }
    private static Dictionary<Type, Func<string, object>> dic;
    private static Queue<string> sc;
    public static T Next<T>() { if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item); return (T)dic[typeof(T)](sc.Dequeue()); }
    public const int MOD = 1000000007;
}

public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1 { get; set; }
    public T2 v2 { get; set; }
    public Pair() { v1 = Input.Next<T1>(); v2 = Input.Next<T2>(); }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public Pair<T1, T2, T3> Push<T3>(T3 val)
        => new Pair<T1, T2, T3>(v1, v2, val);
    public override string ToString()
        => $"{v1.ToString()} {v2.ToString()}";
    public override bool Equals(object obj)
        => this == (Pair<T1, T2>)obj;
    public override int GetHashCode()
        => v1.GetHashCode() ^ v2.GetHashCode();
    public static bool operator ==(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == 0;
    public static bool operator !=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != 0;
    public static bool operator >(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == 1;
    public static bool operator >=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != -1;
    public static bool operator <(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == -1;
    public static bool operator <=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != 1;
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3 { get; set; }
    public Pair() : base() { v3 = Input.Next<T3>(); }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString()
        => $"{base.ToString()} {v3.ToString()}";
}