2417 - Counting Coprime Pairs.cpp

/*
Problem Name: Counting Coprime Pairs
Problem Link: https://cses.fi/problemset/task/2417
Author: Sachin Srivastava (mrsac7)
*/
#include<bits/stdc++.h>
using namespace std;

#define int long long
#define endl '\n'

const int mxN = 1e6+6;
int spf[mxN];

void sieve() {
    spf[0] = 1;
    for (int i = 1; i < mxN; i++)
        spf[i] = i;
    for (int i = 2; i*i < mxN; i++) {
        if (spf[i] == i) {
            for (int j = i*i; j < mxN; j += i) {
                if (spf[j] == j)
                    spf[j] = i;
            }
        }
    }
}

int cnt[mxN];

signed main(){
    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    #ifdef LOCAL
    freopen("input.txt", "r" , stdin);
    freopen("output.txt", "w", stdout);
    #endif
    
    int n; cin>>n;
    int ans = 0;
    sieve();
    for (int i = 0; i < n; i++) {
        int x; cin>>x;
        vector<int> v;
        while (x > 1) {
            int y = spf[x];
            v.push_back(y);
            while (x % y == 0)
                x /= y;
        }
        int k = v.size();
        for (int s = 1; s < (1<<k); s++) {
            int p = 1;
            for (int j = 0; j < k; j++) {
                if (s>>j&1) {
                    p *= v[j];
                }
            }
            int sgn = -1;
            if (__builtin_popcount(s)&1) sgn = 1;
            ans += sgn*cnt[p];
            cnt[p]++;
        }
    }
    cout<<n*(n-1)/2 - ans;
}