88 lines
2.9 KiB
Java
88 lines
2.9 KiB
Java
package Maths;
|
|
|
|
/**
|
|
* Amicable numbers are two different numbers so related
|
|
* 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>
|
|
* * link: https://en.wikipedia.org/wiki/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 and the Sum of that is. Yes right you probably expected it 220
|
|
*/
|
|
|
|
public class AmicableNumber {
|
|
|
|
public static void main(String[] args) {
|
|
|
|
AmicableNumber.findAllInRange(1,3000);
|
|
/* Res -> Int Range of 1 till 3000there are 3Amicable_numbers These are 1: = ( 220,284) 2: = ( 1184,1210)
|
|
3: = ( 2620,2924) So it worked */
|
|
|
|
}
|
|
|
|
/**
|
|
* @param startValue
|
|
* @param stopValue
|
|
* @return
|
|
*/
|
|
static void findAllInRange(int startValue, int stopValue) {
|
|
|
|
/* the 2 for loops are to avoid to double check tuple. For example (200,100) and (100,200) is the same calculation
|
|
* also to avoid is to check the number with it self. a number with itself is always a AmicableNumber
|
|
* */
|
|
StringBuilder res = new StringBuilder();
|
|
int countofRes = 0;
|
|
|
|
for (int i = startValue; i < stopValue; i++) {
|
|
for (int j = i + 1; j <= stopValue; j++) {
|
|
if (isAmicableNumber(i, j)) {
|
|
countofRes++;
|
|
res.append("" + countofRes + ": = ( " + i + "," + j + ")" + "\t");
|
|
}
|
|
}
|
|
}
|
|
res.insert(0, "Int Range of " + startValue + " till " + stopValue + " there are " + countofRes + " Amicable_numbers.These are \n ");
|
|
System.out.println(res.toString());
|
|
}
|
|
|
|
/**
|
|
* Check if {@code numberOne and numberTwo } are AmicableNumbers or not
|
|
*
|
|
* @param numberOne numberTwo
|
|
* @return {@code true} if {@code numberOne numberTwo} isAmicableNumbers otherwise false
|
|
*/
|
|
static boolean isAmicableNumber(int numberOne, int numberTwo) {
|
|
|
|
return ((recursiveCalcOfDividerSum(numberOne, numberOne) == numberTwo && numberOne == recursiveCalcOfDividerSum(numberTwo, numberTwo)));
|
|
}
|
|
|
|
/**
|
|
* calculated in recursive calls the Sum of all the Dividers beside it self
|
|
*
|
|
* @param number div = the next to test dividely by using the modulo operator
|
|
* @return sum of all the dividers
|
|
*/
|
|
static int recursiveCalcOfDividerSum(int number, int div) {
|
|
|
|
if (div == 1) {
|
|
return 0;
|
|
} else if (number % --div == 0) {
|
|
return recursiveCalcOfDividerSum(number, div) + div;
|
|
} else {
|
|
return recursiveCalcOfDividerSum(number, div);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
}
|