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 Python (3.4.3) (judge verdict: Wrong Answer)

n = int(input())
a = list(map(int, input().split()))

a.insert(0, 0)
p = (n+1)*[0]
for i in range(1,n+1):
    for j in range(i,n+1,i):
        p[i] += a[j]
#print(p[1:n+1])

for m in range(1000000):
    flag = 0
    for i in range(n,0,-1):
        if p[i] < 0:
            flag = 1
            l = n // i * i
            for j in range(l,0,-i):
                if p[j] != 0:
                    for k in range(1,j+1):
                        if j % k == 0:
                            p[k] -= p[j]
            break
#    print(p[1:])
    if flag == 0:
        break
#print(p[1:n+1])
print(p[1])