HDU 2608 : 0 or 1 ( 数论：唯一分解定理）
Solving problem is a interesting thing. DragonLee like to slove different problembecause he think it is a way let him more intelligent. But as we knowDragonLee is weak in math. When he come up against a difficult math problem he always try to get a hand.
Now the problem is coming! Let we define T(n) as the sum of all numbers which are positive integers can divied n. and S(n) = T(1) + T(2) + T(3)+...+T(n).
Input
The first line of the input contains an integer T which means the number of test cases. Then T lines follow each line consists of only one positive integers n. You may assume the integer will not exceed 2^31.
Output
For each test case you should output one lines of one integer S(n) %2. So you may see the answer is always 0 or 1 .
Sample Input
copy
3 1 2 3
Sample Output
copy
1 0 0
HINT
S(3) = T(1) + T(2) +T(3) = 1 + (1+2) + (1+3) = 8
S(3) % 2 = 0
Code:（定理）任意一个合数（非素数），都能写成任意素数幂的乘积形式 ，即 n=p1^a1 * p2^a2 . . .*pn^an
（应用）求出数n的因子个数 ：（1+a1）*(1+a2)*(1+a3)*(1+a4)......*(1+an)
（应用）求所有的因子之和：（p1^0+p1^1+p1^2.....p1^a1）*（p2^0+p2^1+p2^2.....p2^a2）*........*（pn^0+pn^n+pn^2.....pn^an）
#include <iostream>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <cstdio>
#include <set>
#include <math.h>
#include <algorithm>
#include <queue>
#include <iomanip>
#include <ctime>
#define ind 0x3f3f3f3f
#define ll long long
using namespace std;
const int mxn = 1e6;
int n,m,k,ans,cnt,cs,a[mxn];
int main()
{
ll col;
cin>>n;
while(n--)
{
cin>>col;
cout<< ( (int)sqrt(col*1.0)%2 + (int)sqrt(col/2.0)%2 )%2<<endl;
}
return 0;
}
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所遇皆星河
