Added program to check Smith number (#6955)

added smith number program

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

@@ -0,0 +1,52 @@
+package com.thealgorithms.maths;
+
+import com.thealgorithms.maths.Prime.PrimeCheck;
+
+/**
+ * In number theory, a smith number  is a composite number for which, in a given number base,
+ *  the sum of its digits is equal to the sum of the digits in its prime factorization in the same base.
+ *
+ * For example, in base 10, 378 = 21 X 33 X 71 is a Smith number since 3 + 7 + 8 = 2 X 1 + 3 X 3 + 7 X 1,
+ * and 22 = 21 X 111 is a Smith number, because 2 + 2 = 2 X 1 + (1 + 1) X 1.
+ *
+ * Wiki: https://en.wikipedia.org/wiki/Smith_number
+ */
+public final class SmithNumber {
+
+    private SmithNumber() {
+    }
+
+    private static int primeFactorDigitSum(int n) {
+        int sum = 0;
+        int num = n;
+
+        // Factorize the number using trial division
+        for (int i = 2; i * i <= num; i++) {
+            while (n % i == 0) { // while i divides n
+                sum += SumOfDigits.sumOfDigits(i); // add sum of digits of factor
+                n /= i; // divide n by the factor
+            }
+        }
+
+        // If n is still > 1, it itself is a prime factor
+        if (n > 1) {
+            sum += SumOfDigits.sumOfDigits(n);
+        }
+
+        return sum;
+    }
+
+    /**
+     * Check if {@code number} is Smith number or not
+     *
+     * @param number the number
+     * @return {@code true} if {@code number} is a Smith number, otherwise false
+     */
+    public static boolean isSmithNumber(int number) {
+        if (PrimeCheck.isPrime(number)) {
+            return false; // Smith numbers must be composite
+        }
+
+        return SumOfDigits.sumOfDigits(number) == primeFactorDigitSum(number);
+    }
+}