（Problem 12）Highly divisible triangular number

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最新推荐文章于 2022-04-19 22:02:36 发布

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分类专栏：欧拉计划(C语言) 文章标签： c 欧拉计划题解

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本文探讨了如何通过编程找出首个拥有多于五百个因数的三角数。文章提供了一段C语言代码，该代码实现了计算三角数及判断其是否具有超过五百个因数的功能，并最终给出了答案为76576500。

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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 <stdio.h> 
#include <stdbool.h>

int trinumber(int n)
{
	if(n % 2 == 0) {
		return (n / 2) * (n + 1);
	} else {
		return ((n + 1) / 2) * n;
	}
}

bool divnum(int n)
{
	int i, sum = 0;
	for(i = 1; i * i < n; i++) {
		if(n % i == 0) {
			sum += 2;
		}
	}
	if(i * i == n) sum++;
	if(sum > 500) return true;
	else return false;
}

void solve(void)
{
	int i, num;
	num = 0;
	for(i = 1; ; i++) {
		if(divnum(trinumber(i))) {
			printf("%d\n",trinumber(i));
			break;
		}
	}
}

int main(void)
{
	solve();
	return 0;
}

Answer:

76576500