ProperDivisors | Topcoder Archive

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

```
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
```
```
12
```
```
2
```
```
Returns: 8
```
```
1000000
```
```
10000000
```
```
10
```
```
Returns: 146066338
```

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