Problem Statement

Let X and Y be positive integers. We say that Y is a divisor of X if and only if there is a positive integer Z such that X = Y*Z. You will be given a String[] numbers. Each element in this String[] will contain a positive integer. For each of the given integers compute the sum of its positive divisors, itself excluded. Return a String[] containing the computed sums in the same order, with no unnecessary leading zeroes.

Definition

Class:              PerfectNumbers
Method:             sumDivisors
Parameters:         String[]
Returns:            String[]
Method signature:   String[] sumDivisors(String[] numbers)
(be sure your method is public)

Notes

All the numbers in the input, and all the numbers you should output will fit into 64-bit signed integer variables.

Constraints

• numbers will contain between 1 and 50 elements, inclusive.
• Each element in numbers contains between 1 and 13 digits ('0'-'9'), inclusive.
• No element in numbers will contain leading zeroes.

Examples

0)

{"6"}
Returns: {"6" }
The divisors of 6 (other than 6 itself) are 1, 2, and 3. Their sum is 1+2+3 = 6.

1)

{"28"}
Returns: {"28" }
Divisors of 28 are 1, 2, 4, 7, and 14, and their sum is 1+2+4+7+14 = 28.
2)

{"4", "8", "16", "32"}
Returns: {"3", "7", "15", "31" }

3)

{"13", "47", "997"}
Returns: {"1", "1", "1" }

4)

{"510510"}
Returns: {"1231314" }
510510 = 2*3*5*7*11*13*17
5)

{"235152", "235326326132", "1234567890123"}
Returns: {"461232", "176530725964", "411987510213" }

6)

{"9999999999999"}
Returns: {"4903272088641" }
This is the largest valid input number.
7)

{"1"}
Returns: {"0" }
And this is the smallest valid input.

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