Added extended version of linear sieve

Author: fredbr

math/linear_sieve_ext.cpp

@@ -0,0 +1,43 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+const int maxn = 10101010;
+
+int cnt[maxn], lp[maxn];
+
+void sieve(int n)
+{
+	vector<int> pr;
+	for (int i = 2; i <= n; i++) {
+		if (lp[i] == 0) {
+			cnt[i] = 1;
+			lp[i] = i;
+			pr.push_back(i);
+		}
+
+		for (int p : pr) {
+			if (p > lp[i] or p*i > n) break;
+
+			lp[p*i] = p;
+			
+			if (i%p == 0) {
+				cnt[i*p] = cnt[i]+1; 
+			}
+			else {			
+				cnt[i*p] = 1;
+			}
+		}
+	}
+}
+
+int main()
+{
+	int n;
+	cin >> n;
+
+	sieve(n);
+
+	for (int i = 1; i <= n; i++)
+		cout << i << " : " << lp[i]  << "^" << cnt[i] << "\n";
+}