Add FriendlyNumber Implementation (#7474)

feat: Add FriendlyNumber Implementation

Author: Rosander0

src/main/java/com/thealgorithms/maths/FriendlyNumber.java

@@ -0,0 +1,49 @@
+package com.thealgorithms.maths;
+
+/**
+ * Two numbers are Friendly if they share the same abundancy index,
+ * which is the ratio of the sum of divisors to the number itself.
+ * Example: 6 and 28 are friendly because sigma(6)/6 = 2 and sigma(28)/28 = 2
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Friendly_number">
+ *     Wikipedia: Friendly Number</a>
+ *
+ * @author Vraj Prajapati @Rosander0
+ */
+public final class FriendlyNumber {
+
+    private FriendlyNumber() {
+        // Utility class
+    }
+
+    private static int sumOfDivisors(final int number) {
+        int sum = 0;
+        final int root = (int) Math.sqrt(number);
+        for (int i = 1; i <= root; i++) {
+            if (number % i == 0) {
+                sum += i;
+                final int other = number / i;
+                if (other != i) {
+                    sum += other;
+                }
+            }
+        }
+        return sum;
+    }
+
+    /**
+     * Checks whether two numbers are Friendly Numbers.
+     *
+     * @param a First number (must be positive)
+     * @param b Second number (must be positive)
+     * @return true if a and b are friendly numbers, false otherwise
+     */
+    public static boolean areFriendly(final int a, final int b) {
+        if (a <= 0 || b <= 0) {
+            return false;
+        }
+        final long sigmaA = sumOfDivisors(a);
+        final long sigmaB = sumOfDivisors(b);
+        return sigmaA * b == sigmaB * a;
+    }
+}

src/test/java/com/thealgorithms/maths/FriendlyNumberTest.java

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+package com.thealgorithms.maths;
+// author: Vraj Prajapati @Rosander0
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+public class FriendlyNumberTest {
+
+    @Test
+    public void testFriendlyNumbers() {
+        // 6 and 28 are friendly (abundancy index = 2)
+        assertTrue(FriendlyNumber.areFriendly(6, 28));
+        // Every number is friendly with itself
+        assertTrue(FriendlyNumber.areFriendly(6, 6));
+        assertTrue(FriendlyNumber.areFriendly(1, 1));
+    }
+
+    @Test
+    public void testNonFriendlyNumbers() {
+        assertFalse(FriendlyNumber.areFriendly(6, 10));
+        assertFalse(FriendlyNumber.areFriendly(10, 15));
+        assertFalse(FriendlyNumber.areFriendly(4, 9));
+    }
+
+    @Test
+    public void testInvalidInputs() {
+        assertFalse(FriendlyNumber.areFriendly(0, 6));
+        assertFalse(FriendlyNumber.areFriendly(-1, 6));
+        assertFalse(FriendlyNumber.areFriendly(6, -1));
+    }
+}