Problem 12(Highly divisible triangular number)

Problem 12(Highly divisible triangular number)

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th 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?

In Python:

#PE12 Highly divisible triangular number
import time


def divcount(n):
    result = 1
    for i in range(2, int(n / 2) + 1):
        count = 0
        while n % i == 0:
            n /= i
            count += 1
        result *= (count + 1)
        if n == 1:
            break
    if result == 1:
        return 2
    else:
        return result


start_time = time.time()
triangular = 1
i = 2

while divcount(triangular) < 500:
    triangular = triangular + i
    i += 1
print(triangular)
print(time.time() - start_time, "seconds")

Run time: 5.669299840927124 seconds

In Python:

//Euler12 Highly divisible triangular number

package project_euler;

public class Euler12 {

public static int divCount(long n) {

int count = 0;

int result = 1;

long num = n;

for (int i = 2; i < Math.ceil(n / 2) + 1; i++) {

count  = 0;

while (num % i == 0) {

num /= i;

count++;

}

result *= count + 1;

if (num == 1) break;

}

if (result == 1) {

return 2;

}

else {

return result;

}

}

public static void main(String[] args) {

long startTime = System.currentTimeMillis();

long triangular = 1;

int i = 2;

while (divCount(triangular) < 500) {

triangular += i;

i++;

}

System.out.println(triangular);

long endTime = System.currentTimeMillis();

System.out.println((double)(endTime - startTime)/(double)1000 + "seconds");

}

}

Run time: 0.36seconds

Solution: 76576500

[from Project Euler: https://projecteuler.net/problem=12]