PowerfulNumbers | Topcoder Archive

Problem Statement

In this problem you are to find the smallest number, N, such that for each element p of powers, there is some distinct integer k > 1 such that k^p is a factor of N. That is, N%(k^p) == 0 using a different value of k for each element of powers.

Definition

Class:: PowerfulNumbers
Method:: smallest
Parameters:: int[]
Returns:: long
Method signature:: long smallest(int[] powers)
(be sure your method is public)

Constraints

power will contain between 1 and 10 elements greater than 1, inclusive.
The return value will fit in a long.

Examples

```
{2,2,2}
```
```
Returns: 36
```
22, 32, and 62 are all factors of 36.
```
{2,3,4}
```
```
Returns: 64
```
```
{2,3,4,4,4}
```
```
Returns: 4096
```

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