Lightoj 1336 Sigma Function (number theory integer splitting inference)

---Test instructions: To define a function, F (n) represents the sum of all the approximations of N, and gives the integer split formula and the calculation method of f (n), and for a given n let us ask how many 1-n between the number of F (x) to be an even number of cases, the output.

---Analysis: to consider the case of F (x) is odd, given the formula given to us in the topic, if f (x) is an odd number, then any of the polynomial inside must be odd, you can know P = 2 o'clock, p^e-1 is definitely odd, if p! = 2, when and only if E is an even number, this is an odd number, which proves as follows:

The original variant is [p^ (e+1)-P + (p-1)]/(p-1) = p* (p^e-1)/(p-1) + 1;

So p/(p-1) = 1, p^e must be odd (because P is prime, prime numbers are definitely odd), so p^e-1 is an even number, so the underscore is definitely odd, proving to be true.

Then the formula in the title can be written in the following form:

2^k0 * 3^ (2*K1) * 5^ (2*K2) * ... * pn^ (2*KN); the underscore can be expressed as num ^ 2;

And k0>=0, so the solution satisfying the condition is num^2 and 2 * num^2, because the higher power of satisfying 2 must also be a multiple of 2, and cannot be computed repeatedly. The code is as follows:

--"NOTE: This topic can not be directly recycled, although the topic given a long time, but the direct violence will still be super, here direct calculation, sqrt can not be forced to convert to ll, but this problem l also enough;

--"sentiment: The problem of number theory is the code is very short, but the amount of thinking and proof of the kind of super ..."

#include<cstring>
#include<cstdio>
#include<cmath>
#include<iostream>
using namespace std;
#define L long
int main()
{
    int t,ca = 0;
    long long n;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lld",&n);
        L ans = 0;
        double tmp = n;
        ans = L(sqrt(tmp)) + L(sqrt(tmp/2));
        printf("Case %d: %ld\n",++ca,n-ans);
    }
    return 0;
}

Lightoj 1336 Sigma Function (number theory integer splitting inference)