### Problem Statement

An integer k greater than 0 is called a cool divisor of m if it is less than m and divides m, but k^n does not divide m. Let d(m) denote the number of cool divisors that exist for an integer m. Given two integers a and b return the sum d(a) + d(a + 1) + ... + d(a + b).

### Definition

 Class: ProperDivisors Method: analyzeInterval Parameters: int, int, int Returns: int Method signature: int analyzeInterval(int a, int b, int n) (be sure your method is public)

### Notes

-The result will always fit into a signed 32-bit integer.

### Constraints

-a will be between 1 and 1000000 (10^6), inclusive.
-b will be between 1 and 10000000 (10^7), inclusive.
-n will be between 2 and 10, inclusive.

### Examples

0)

 `32` `1` `3`
`Returns: 5`
 The cool divisors of 32 are 4, 8 and 16 so d(32) = 3; the cool divisors of 33 are 3 and 11 so d(33) = 2. Hence the desired sum d(32) + d(33) = 3 + 2 = 5.
1)

 `1` `12` `2`
`Returns: 8`
2)

 `1000000` `10000000` `10`
`Returns: 146066338`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8547

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=11128&pm=8547

Xixas

#### Testers:

PabloGilberto , Olexiy , marek.cygan , ivan_metelsky

#### Problem categories:

Math, Simple Search, Iteration