Chapter 2: find the box array, complete number in the specified interval, and improve the complete number in the specified interval

// Find the box array 
int main()
{
    
	long a, b, d, k, x, y, z, w;
	printf("  Please enter the interval [a,b] The upper and lower a,b:");
	scanf("%ld, %ld", &a, &b);
	k = 0;
	for (x = a; x <= sqrt(b*b / 3); x++) // Set enumeration triple loop  
	for (y = x; y <= sqrt((b*b-x*x) /2);y++) 
	for (z = y; z <= sqrt(b*b - x * x - y * y); z++)
		{
    
			d = x * x + y * y + z * z;
			w = (int)sqrt(d); //" by ×、,、z The sum of squares of  
			if (w > b) break;
			if (w * w == d) //  Compare the best value when the conditions are met 
			{
    
				k++; // Output the maximum value  
				printf("%3d: %1d,%1d, %ld, %1d \n", k, x, y, z, w);
			}
		}
	if (k > 0)
		printf(" In the specified interval 【%ld,%ld】 There are more than %ld Number of boxes in group ",a,b,k);
	else printf(" There is no number of boxes in the specified range \n");
	return 0;
}

result ：

// Specify the perfect number in the interval 
int main()
{
    
	int k;
	long a, s, x, y;
	printf("  please enter an integer  x,y：");
	scanf ("%ld, %ld", &x, &y);
	printf("[%1d,%1d] The perfect number in has ：\n", x, y);
	for (a = x; a <= y; a++)
	{
    
		s = 1;
		for (k = 2; k <= a / 2; k++) //  Try to find a The factor of k 
			if (a%k == 0) s = s + k; //k yes a The factor of , Sum of assignment  
		if (a == s)
		{
    
			printf("%ld = 1", a); // Print the sum of factors from small to large 
			for (k = 2; k <= a / 2; k++)
				if (a%k == 0) printf("+%d", k);
			if (a % 2 == 1) printf("  Find the odd number ！");
			printf("\n");
		}
	}
	return 0;
}

result ：

// Explore perfect numbers and P- Perfect number 
int main()
{
    
	int k; 
	long a, b, s, x, y; 
	printf("  Find interval [x,y] The perfect number in .");
	printf("  please enter an integer x, y： ");
	scanf("%ld",&x);
	scanf("%ld",&y);
	printf("[ %1d, %1d ] The perfect number in has ：\n",x,y);
			for (a = x; a <= y; a++)
			{
    
				s = 1;
				b = sqrt(a);
				for (k = 2; k <= b; k++)
					if (a%k == 0) s = s + k + a / k; //  Try to find a The factor of k 
				if (a == b * b) 
					s = s - b; //k And alk yes a The factor of  //  If a=b^2, Remove a repetition factor b 
				if (a == s)
				{
    
					printf("%ld = 1", a); // Print a The factor sum formula of  
					for (k = 2; k <= a / 2; k++)
						if (a%k == 0) printf("+%d", k);
					if (a % 2 == 1)printf(" Odd perfect number ！");
					printf("\n");
				}
			}
			return 0;
}

result ：

int main()
{
    
	double a, a1, s, b, c, d, d1, k, t, t1, x, y, p[10], q[10], min; 
	int j, m = 0;
	min = 1.0;
	printf("  Please enter the interval x,y："); 
		scanf ("%lf", &x) ;
		scanf("%lf", &y);
		// Enumerate all integers in the interval a
		for (a = x; a <= y; a++)
		{
    
			s = 1;
			b = floor(sqrt(a)); //  Try to find a The factor of k
			for (k = 2; k <= b; k++)
				if (fmod(a, k) == 0)
					s = s + k + a / k;
			if (a == b * b)
				s = s - b; //k And a/k yes a The factor of , Sum up  // If a-b°2, Remove the repetition factor b 
			t = s / a;
			d = floor(t);
			c = t - d;
			if (c == 0)
			{
    
				m++;
				p[m] = a;
				q[m] = t;

			}
			else if (c > 0.5)
			{
    
				c = 1 - c;
				d = d + 1;
			}
			if (t > 0.5 && c < min)
			{
    
				min = c;
				a1 = a;
				t1 = t;
				d1 = d;
			}
		}
	if (m > 0)
		for (j = 1; j <= m; j++)
			printf(" p(%.0f) = %.0f", p[j], q[j]);
	else
			printf(" %.0f Factor ratio of %.4f The nearest positive integer %.0f\n",a1,t1,d1);
			return 0;
}

result ：