number of (l, r) such that 0<=l <= r <= n-1 and gcd(arr[l], arr[l+1] . . . arr[r]) = 1 using sparse table

gcd1_sparseTable.cpp

#include <bits/stdc++.h>

using namespace std;

#define ll long long
#define pint pair<int, int>
#define pll pair<ll, ll>
#define mk(a, b) make_pair(a, b)
#define pr(n) printf("%d\n", n)
#define sc(n) scanf ("%d", &n)
#define scll(n) scanf ("%lld", &n)
#define prll(n) printf("%lld\n", n)
#define MOD 1000000007ll

int n, q;
int arr[100000];
int table[100000][16+1];  // 2^16 > 10e5
int k = 16;

void buildTable () {
	int i;
	for (i = 0; i < n; i++) {
		table[i][0] = arr[i];
	}
	int j;
	for (j = 1; j <= k; j++) {
		for (i = 0; i <= n-(1<<j); i++) {
			table[i][j] = __gcd(table[i][j-1] , table[i+(1<<(j-1))][j-1]);
		}
	}
	return ;
}

int getQuery() {
	int i;
	int ans = 0;
	int temp;
	int j;
	int g;
	for (i = 0; i < n; i++) {
		temp = i;
		g = 0;
		for (j = k; j >= 0; j--) {
			if (temp+(1<<j)-1 < n) {
				if (__gcd(g, table[temp][j]) > 1) {
					temp = temp + (1<<j);
				}
			}
		}
		if(temp < n)
		ans += (n-temp);
	}

	return ans;
}

int main (void) {
	sc(n);
	int i;
	for (i = 0; i < n; i++) {
		sc(arr[i]);
	}
	buildTable();
	cout<<getQuery()<<endl;
	return 0;
}