#### Amicable Number

P
```package com.thealgorithms.maths;

import java.util.Set;
import org.apache.commons.lang3.tuple.Pair;

/**
* Amicable numbers are two different natural numbers that the sum of the
* proper divisors of each is equal to the other number.
* (A proper divisor of a number is a positive factor of that number other than the number itself.
* For example, the proper divisors of 6 are 1, 2, and 3.)
* A pair of amicable numbers constitutes an aliquot sequence of period 2.
* It is unknown if there are infinitely many pairs of amicable numbers.
*
* <p>
* <p>
* Simple Example: (220, 284)
* 220 is divisible by {1,2,4,5,10,11,20,22,44,55,110} <-SUM = 284
* 284 is divisible by {1,2,4,71,142} <-SUM = 220.
*/
public class AmicableNumber {
/**
* Finds all the amicable numbers in a given range.
*
* @param from range start value
* @param to   range end value (inclusive)
* @return list with amicable numbers found in given range.
*/
public static Set<Pair<Integer, Integer>> findAllInRange(int from, int to) {
if (from <= 0 || to <= 0 || to < from) {
throw new IllegalArgumentException("Given range of values is invalid!");
}

Set<Pair<Integer, Integer>> result = new LinkedHashSet<>();

for (int i = from; i < to; i++) {
for (int j = i + 1; j <= to; j++) {
if (isAmicableNumber(i, j)) {
}
}
}
return result;
}

/**
* Checks whether 2 numbers are AmicableNumbers or not.
*/
public static boolean isAmicableNumber(int a, int b) {
if (a <= 0 || b <= 0) {
throw new IllegalArgumentException("Input numbers must be natural!");
}
return sumOfDividers(a, a) == b && sumOfDividers(b, b) == a;
}

/**
* Recursively calculates the sum of all dividers for a given number excluding the divider itself.
*/
private static int sumOfDividers(int number, int divisor) {
if (divisor == 1) {
return 0;
} else if (number % --divisor == 0) {
return sumOfDividers(number, divisor) + divisor;
} else {
return sumOfDividers(number, divisor);
}
}
}
```  