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 Rust (1.15.1) (judge verdict: Accepted)

/// Thank you tanakh!!!
/// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

use std::cmp;
use std::collections::VecDeque;
use std::i64;
use std::usize;

const INF: i64 = 1 << 50;

fn main() {
    input!(n: usize, a: [i64; n]);

    let sum = a.iter().filter(|&&a| a > 0).sum::<i64>();

    let source = n;
    let sink = n + 1;
    let mut dinitz = Dinitz::new(n + 2);
    for i in 0..n {
        if a[i] < 0 {
            dinitz.add_edge(source, i, -a[i]);
        } else {
            dinitz.add_edge(i, sink, a[i]);
        }
    }

    for i in 1..(n + 1) {
        let mut cur = 2 * i;
        while cur <= n {
            dinitz.add_edge(i - 1, cur - 1, INF);
            cur += i;
        }
    }

    let min_cut = dinitz.max_flow(source, sink);
    println!("{}", sum - min_cut);
}

struct Edge {
    pub to: usize,
    pub rev: usize,
    pub cap: i64,
}

pub struct Dinitz {
    g: Vec<Vec<Edge>>,
    level: Vec<i32>,
    iter: Vec<usize>,
}

impl Dinitz {
    pub fn new(v: usize) -> Dinitz {
        let mut g: Vec<Vec<Edge>> = Vec::new();
        for _ in 0..v {
            g.push(Vec::new());
        }
        Dinitz {
            g: g,
            level: vec![0; v],
            iter: vec![0; v],
        }
    }

    pub fn add_edge(&mut self, from: usize, to: usize, cap: i64) {
        let to_len = self.g[to].len();
        let from_len = self.g[from].len();
        self.g[from].push(Edge {
            to: to,
            rev: to_len,
            cap: cap,
        });
        self.g[to].push(Edge {
            to: from,
            rev: from_len,
            cap: 0,
        });
    }

    fn dfs(&mut self, v: usize, t: usize, f: i64) -> i64 {
        if v == t {
            return f;
        }
        while self.iter[v] < self.g[v].len() {
            let (e_cap, e_to, e_rev);
            {
                let ref e = self.g[v][self.iter[v]];
                e_cap = e.cap;
                e_to = e.to;
                e_rev = e.rev;
            }
            if e_cap > 0 && self.level[v] < self.level[e_to] {
                let d = self.dfs(e_to, t, cmp::min(f, e_cap));
                if d > 0 {
                    {
                        let ref mut e = self.g[v][self.iter[v]];
                        e.cap -= d;
                    }
                    {
                        let ref mut rev_edge = self.g[e_to][e_rev];
                        rev_edge.cap += d;
                    }
                    return d;
                }
            }
            self.iter[v] += 1;
        }

        return 0;
    }

    fn bfs(&mut self, s: usize) {
        let v = self.level.len();
        self.level = vec![-1; v];
        self.level[s] = 0;
        let mut deque = VecDeque::new();
        deque.push_back(s);
        while !deque.is_empty() {
            let v = deque.pop_front().unwrap();
            for e in &self.g[v] {
                if e.cap > 0 && self.level[e.to] < 0 {
                    self.level[e.to] = self.level[v] + 1;
                    deque.push_back(e.to);
                }
            }
        }
    }

    pub fn max_flow(&mut self, s: usize, t: usize) -> i64 {
        let v = self.level.len();
        let mut flow: i64 = 0;
        loop {
            self.bfs(s);
            if self.level[t] < 0 {
                return flow;
            }
            self.iter = vec![0; v];
            loop {
                let f = self.dfs(s, t, i64::MAX);
                if f == 0 {
                    break;
                }
                flow += f;
            }
        }
    }
}