Project Euler: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?

#include <iostream>
using namespace std;

int divi(long long a)
{
	int res = 0;
	for (int i = 1; i <= a; i++)
	{
		if (a%i == 0)
			res++;
	}
	return res;
}

int main()
{
	long long count = 0;
	for (int i = 1; i <= 10000000; i++)
	{
		count += i;
		if (divi(count) >= 500)
			break;
		//cout << i << endl;
	}
	printf("%lld\n", count);
	system("pause");
	return 0;
}

虽然能算出结果但是真的好慢。

任何整数都可以质因数分解成 N=p1^a1 * p2^a2 * p3^a3 * ...

则N的因子个数为(a1+1)*(a2+1)*(a3+1)*....

#include <iostream>
#include <map>
using namespace std;

int divi(long long a)
{
	int res = 1;
	map<int, int> mp;
	for (int i = 2; i <= a; i++)
	{
		while (a != i)
		{
			if (a%i == 0)
			{
				mp[i]++;
				a = a / i;
			}
			else
				break;
		}
	}
	if (a != 1)
		mp[a]++;
	map<int, int>::iterator iter = mp.begin();
	for (iter = mp.begin(); iter != mp.end(); iter++)
	{
		//cout << iter->first << " " << iter->second << endl;
		res = res*(iter->second + 1);
	}
	return res;
}

int main()
{
	long long count = 0;
	for (int i = 1; i <= 10000000; i++)
	{
		count += i;
		if (divi(count) >= 500)
			break;
		//cout << i << endl;
	}
	printf("%lld\n", count);
	system("pause");
	return 0;
}