Highly divisible triangular number

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

 1: 1
 3: 1,3
 6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

Solution:


void Solution()
        {
            int i = 1;
            int triangleNumber = 0;
            do
            {
                triangleNumber = i * (i + 1) / 2;
                i++;
            }
            while (NoOfDivisors(triangleNumber) <= 500);

            Console.WriteLine(triangleNumber);
        }

        static int NoOfDivisors(int num)
        {
            //Based on the formula, otherwise it will take infinite time
            //Let d(n) be the number of divisors for the natural number, n.
            //We begin by writing the number as a product of prime factors: n = paqbrc...
            //then the number of divisors, d(n) = (a+1)(b+1)(c+1)...

            int counter = 0;
            int totalCount = 1;
            bool flag = false;
            int tempNum = num;
            for (int i = 2; i <= num / 2; i++)
            {
                if (tempNum % i == 0)
                {
                    counter++;
                    tempNum = tempNum / i;
                    i--;
                    flag = true;
                    continue;

                }
                if (flag)
                {
                    totalCount = totalCount * (counter + 1);
                    counter = 0;
                    flag = false;
                }
                if (tempNum == 1)
                    break;
            }

            return totalCount;
        }

No comments :

Post a Comment

Comment Here