PerfectNumbers | Topcoder Archive

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

```
{"6"}
```
```
Returns: {"6" }
```
The divisors of 6 (other than 6 itself) are 1, 2, and 3. Their sum is 1+2+3 = 6.
```
{"28"}
```
```
Returns: {"28" }
```
Divisors of 28 are 1, 2, 4, 7, and 14, and their sum is 1+2+4+7+14 = 28.

{"4", "8", "16", "32"}

Returns: {"3", "7", "15", "31" }

{"13", "47", "997"}

Returns: {"1", "1", "1" }

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

{"235152", "235326326132", "1234567890123"}

Returns: {"461232", "176530725964", "411987510213" }

{"9999999999999"}

Returns: {"4903272088641" }

This is the largest valid input number.

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

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