Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

49愛的鼓勵 6訂閱站台

The early Greeks have made great contributions to the field of mathematics. Among the great mathematicians of this times were Euclid and Pythagoras. The 23 volume Elements of Euclid is still regarded as on of the cornerstones in the study of mathematics.

Euclid made an important contributions to a problem posed by Pythagoras - that of finding all the perfect numbers. The number 6 is called a perfect number because 6 = 1 + 2 + 3, the sum of all its proper divisors, (i.e. divisors less than 6). Another example of a perfect number is 28, because 28 = 1 + 2 + 4 + 7 + 14, and 1, 2, 4, 7 and 14 are the divisors of 28 less than 28.

In Book IX of the `Elements' Euclid found all the even perfect numbers. (It has been proven later much later, in the 20-th century that all perfect numbers are even.) Euclid proved that an even number is perfect if it has the form

where both p and 2^p - 1 are prime numbers.

Two thousand years later, Leonhard Euler proved the converse of Euclid's theorem. That is every even perfect number must be of Euclid's type. For example, for 6 and 28, we have

Perfect numbers are very rare. By 1975, only 24 perfect numbers have been discovered. The first four perfect numbers are

6, 28, 496, and 8128

which correspond to the following values of p

2, 3, 5, and 7.

You would be given several integer numbers p, which would not necessarily be prime numbers. You have to determine if 2^p-1(2^p - 1) is a perfect number. The largest perfect number in this problem will not exceed 2³³.

Input 

The input contains two lines of integers. The first line contains the number of integers appearing on the second line. The second line contains the values of p that should be tested.

Output 

For each integer value to be tested output ``Yes" or ``No" on a line of its own. The output will be ``Yes" if the integer value p generates a perfect number and ``No" otherwise.

Sample Input 

  
6 
2,3,4,5,6,7

Sample Output 

  
Yes 
Yes 
No 
Yes 
No 
Yes

---

看網路上公布的做法，感覺會 overflow 的說，對於 2^33。
至於梅森質數直接去 wiki 打表

#include <stdio.h>
#include <map>
using namespace std;
int main() {
    //http://zh.wikipedia.org/wiki/%E6%A2%85%E6%A3%AE%E7%B4%A0%E6%95%B0
    map<int, int> R;
    int A[] = {2, 3, 5, 7, 13, 17, 31, 61, 89};
    int n, x, i;
    for(i = 0; i < 9; i++)
        R[A[i]] = 1;
    while(scanf("%d", &n) == 1) {
        for(i = 0; i < n; i++) {
            scanf("%d", &x);
            int flag = R[x];
            puts(flag ? "Yes" : "No");
            getchar();
        }
    }
    return 0;
}