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Main.java
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Main.java
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import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
/*
@author: mces58
Problem 21
Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under 10000.
Answer: 31626
*/
public class Main {
// Keep a map of the sums of divisors for all numbers seen so far
static Map<Integer, Integer> divisorSums = new HashMap<Integer, Integer>();
public static void main(String[] args) {
HashSet<Integer> amicables = new HashSet<Integer>();
int amicableSum = 0;
for (int i = 1; i < 10000; i++) {
if (amicables.contains(i)) {
continue;
}
int b = d(i);
if (d(b) == i && b > i) {
amicables.add(i);
amicables.add(b);
amicableSum += i + b;
}
}
System.out.println(amicableSum);
}
// Calculate the sum of proper divisors of n
public static int d(int n) {
if (divisorSums.containsKey(n)) {
return divisorSums.get(n);
}
int sum = 1;
for (int i = 2; i <= Math.sqrt(n); i++) {
if (n % i == 0) {
sum += i;
if (i != n / i) {
sum += n / i;
}
}
}
divisorSums.put(n, sum);
return sum;
}
}