Problem 12 Highly divisible triangular number （分解因子）

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#Problem 12 #Highly divisible #triangular number #分解因子

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本文探讨了寻找首个拥有超过五百个除数的三角数的问题，并提供了一段C++代码实现，通过逐步增加自然数并计算每个三角数的除数数量来找到目标数值。

Highly divisible triangular number

Problem 12

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?

Answer:

76576500

代码：

#include<bits/stdc++.h>
using namespace std;
int Q(int n)
{
	int c = 0;
	int s = (int)sqrt(n);
	for (int x = 1; x <= s; x++)
		if (n%x == 0)
			c++;
	return 2*c;
}
int main()
{
	int ans = 1, n = 2;
	int factors = 1;
	while (factors < 501)
	{
		ans += n;
		n++;
		factors = Q(ans);
	}
	cout<<ans<<endl;
	return 0;
}