feat: Add aliquot sum of a number algorithm, class Math (TheAlgorithm…

…s#2400)

* Added aliquot_sum.cpp

* Fixed indentation and changed argument to ull int

* Fixed type of I

* Made parameter as const

* Made some required changes

* Added changes due to namespace

* Formatting changes

Co-authored-by: David Leal <[email protected]>

math/aliquot_sum.cpp

@@ -0,0 +1,68 @@
+/**
+ * @file
+ * @brief Program to return the [Aliquot
+ * Sum](https://en.wikipedia.org/wiki/Aliquot_sum) of a number
+ *
+ * \details
+ * The Aliquot sum s(n) of a non-negative integer n is the sum of all
+ * proper divisors of n, that is, all the divisors of n, other than itself.
+ * For example, the Aliquot sum of 18 = 1 + 2 + 3 + 6 + 9 = 21
+ *
+ * @author [SpiderMath](https://github.com/SpiderMath)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
+
+/**
+ * @brief Mathematical algorithms
+ * @namespace math
+ */
+namespace math {
+/**
+ * Function to return the aliquot sum of a number
+ * @param num The input number
+ */
+uint64_t aliquot_sum(const uint64_t num) {
+    if (num == 0 || num == 1) {
+        return 0;  // The aliquot sum for 0 and 1 is 0
+    }
+
+    uint64_t sum = 0;
+
+    for (uint64_t i = 1; i <= num / 2; i++) {
+        if (num % i == 0) {
+            sum += i;
+        }
+    }
+
+    return sum;
+}
+}  // namespace math
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // Aliquot sum of 10 is 1 + 2 + 5 = 8
+    assert(math::aliquot_sum(10) == 8);
+    // Aliquot sum of 15 is 1 + 3 + 5 = 9
+    assert(math::aliquot_sum(15) == 9);
+    // Aliquot sum of 1 is 0
+    assert(math::aliquot_sum(1) == 0);
+    // Aliquot sum of 97 is 1 (the aliquot sum of a prime number is 1)
+    assert(math::aliquot_sum(97) == 1);
+
+    std::cout << "All the tests have successfully passed!\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run the self-test implementations
+
+    return 0;
+}