AlmostPerfectNumber | Topcoder Archive

Problem Statement

An integer x is called a proper divisor of an integer y if x is a divisor of y and 1 <= x < y.

Let us denote as s(a) the sum of all proper divisors of a. An integer a is called almost perfect by k if |a-s(a)| <= k.

You are given ints left, right and k. Return the number of integers between left and right, inclusive, that are almost perfect by k.

Definition

Class:: AlmostPerfectNumber
Method:: count
Parameters:: int, int, int
Returns:: int
Method signature:: int count(int left, int right, int k)
(be sure your method is public)

Constraints

left will be between 2 and 1000, inclusive.
right will be between left and 1000, inclusive.
k will be between 0 and 1000, inclusive.

Examples

```
2
```
```
10
```
```
1
```
```
Returns: 4
```
The following numbers between 2 and 10 are almost perfect by 1: 2 (s(2) = 1), 4 (s(4) = 3), 6 (s(6) = 6) and 8 (s(8) = 7).
```
5
```
```
5
```
```
5
```
```
Returns: 1
```
```
11
```
```
20
```
```
50
```
```
Returns: 10
```

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