Step by Step solution about How to resolve the algorithm Perfect numbers step by step in the C# programming language

General Overview: This C# code identifies and prints perfect numbers within the range of 1 to 33,550,337. A perfect number is a positive integer whose sum of all its positive proper divisors (excluding itself) equals the number itself.

First Implementation: Main Method:

• The Main method prints a message indicating that it will find perfect numbers in the specified range.
• It enters a loop to iterate through all numbers from 0 to 33,550,337.

IsPerfect Method:

• The IsPerfect method checks if a given number is perfect.
• It initializes a variable sum to 0.
• It iterates through all numbers from 1 to the number, excluding the number itself.
• For each number i, it checks if num is divisible by i (i.e., num % i == 0). If so, it adds i to sum.
• Finally, it returns if sum is equal to num, indicating that the number is perfect.

Second Implementation: Main Method:

• Same as the first implementation.

IsPerfect Method:

• Uses LINQ to simplify the calculation of the sum of proper divisors.
• It uses the Enumerable.Range method to create a sequence of numbers from 1 to num - 1.
• It applies the Sum method to the sequence, with a lambda expression that checks if num is divisible by each number n and adds n to the running sum if divisible.
• If the resulting sum is equal to num, the method returns true to indicate that the number is perfect.

Usage:

• Both implementations iterate through the entire range of numbers from 1 to 33,550,337.
• For each number, they calculate the sum of its proper divisors using the IsPerfect method.
• If the sum is equal to the number, they print the number as a perfect number.
• The user can interact with the program by pressing any key after the program finishes executing to close the console window.

static void Main(string[] args)
{
	Console.WriteLine("Perfect numbers from 1 to 33550337:");

	for (int x = 0; x < 33550337; x++)
	{
		if (IsPerfect(x))
			Console.WriteLine(x + " is perfect.");
	}

	Console.ReadLine();
}

static bool IsPerfect(int num) 
{
	int sum = 0;
	for (int i = 1; i < num; i++)
	{
		if (num % i == 0)
			sum += i;
	}

	return sum == num ;
}


static void Main(string[] args)
{
	Console.WriteLine("Perfect numbers from 1 to 33550337:");

	for (int x = 0; x < 33550337; x++)
	{
		if (IsPerfect(x))
			Console.WriteLine(x + " is perfect.");
	}

	Console.ReadLine();
}

static bool IsPerfect(int num) 
{
	return Enumerable.Range(1, num - 1).Sum(n => num % n == 0 ? n : 0 ) == num;
}