cf(思维,数学)
2015-10-31 16:04
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B. Duff in Love
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Duff is in love with lovely numbers! A positive integer x is called lovely if
and only if there is no such positive integer a > 1 such that a2 is
a divisor of x.
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present,
Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Sample test(s)
input
output
input
output
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22,
so 12 is not lovely, while 6 is indeedlovely.
数学题,,,,,,,这么简单却仍然想不出来怎么破
真的是很伤、、、、看完代码就知道这题多么多么多么水啊啊啊!!!
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Duff is in love with lovely numbers! A positive integer x is called lovely if
and only if there is no such positive integer a > 1 such that a2 is
a divisor of x.
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present,
Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Sample test(s)
input
10
output
10
input
12
output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22,
so 12 is not lovely, while 6 is indeedlovely.
数学题,,,,,,,这么简单却仍然想不出来怎么破
真的是很伤、、、、看完代码就知道这题多么多么多么水啊啊啊!!!
#include <iostream> #include <stdio.h> #include <math.h> #include<algorithm> using namespace std; int main() { long long n; scanf("%I64d",&n); for(long long i=1;i*i<=n;i++) if(n%(i*i)==0) n/=i,i=1; cout<<n<<endl; return 0; }
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