HDU1323 Prefection

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本文介绍了一个简单的算法，用于判断一个正整数是否为完美数、盈数或亏数。通过计算一个数的所有真因子之和，并与该数本身进行比较，从而确定其属性。文章还提供了一段C语言实现代码作为参考。

1323

Perfection

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2912 Accepted Submission(s): 1785

Problem Description

From the article Number Theory in the 1994 Microsoft Encarta: “If a, b, c are integers such that a = bc, a is called a multiple of b or of c, and b or c is called a divisor or factor of a. If c is not 1/-1, b is called a proper divisor of a. Even integers, which include 0, are multiples of 2, for example, -4, 0, 2, 10; an odd integer is an integer that is not even, for example, -5, 1, 3, 9. A perfect number is a positive integer that is equal to the sum of all its positive, proper divisors; for example, 6, which equals 1 + 2 + 3, and 28, which equals 1 + 2 + 4 + 7 + 14, are perfect numbers. A positive number that is not perfect is imperfect and is deficient or abundant according to whether the sum of its positive, proper divisors is smaller or larger than the number itself. Thus, 9, with proper divisors 1, 3, is deficient; 12, with proper divisors 1, 2, 3, 4, 6, is abundant.”
Given a number, determine if it is perfect, abundant, or deficient.

Input
A list of N positive integers (none greater than 60,000), with 1 < N < 100. A 0 will mark the end of the list.

Output
The first line of output should read PERFECTION OUTPUT. The next N lines of output should list for each input integer whether it is perfect, deficient, or abundant, as shown in the example below. Format counts: the echoed integers should be right justified within the first 5 spaces of the output line, followed by two blank spaces, followed by the description of the integer. The final line of output should read END OF OUTPUT.

Sample Input
15 28 6 56 60000 22 496 0

Sample Output
PERFECTION OUTPUT
15 DEFICIENT
28 PERFECT
6 PERFECT
56 ABUNDANT
60000 ABUNDANT
22 DEFICIENT
496 PERFECT
END OF OUTPUT

Source
Mid-Atlantic USA 1996

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学小学数学的英语题，题目主要求真因子之和，小于自己就是DEFICIENT，等于自己就是PERFECT，大于自己就是ABUNDENT

#include<cstdio>
int main()
{
    int n;
    printf("PERFECTION OUTPUT\n");
    while (scanf("%d",&n), n)
    {
        int sum=1;
        for (int i = 2; i <= n / 2; i++)
            if (n%i == 0)
                sum += i;
        if (sum < n)
            printf("%5d  DEFICIENT\n", n);
        else if (sum == n)
            printf("%5d  PERFECT\n", n);
        else
            printf("%5d  ABUNDANT\n", n);
    }
    printf("END OF OUTPUT\n");
    return 0;
}