complete 1929.cpp 17425.cpp 32870.cpp 11868.rs

storage/zeta/cpp/completed/17425.cpp

@@ -0,0 +1,95 @@
+#include <cmath>
+#include <iostream>
+#include <vector>
+
+#define let auto
+#define fn auto
+#define usize size_t
+using namespace std;
+
+fn fastio() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+}
+
+const let N_MAX = 1'000'000;
+
+let Primes = vector<usize>();
+
+fn generate_primes(usize n) {
+    Primes.clear();
+    Primes.push_back(2);
+    for (usize i = 3; i <= n; i += 2) {
+        for (let p: Primes) {
+            if (i % p == 0) {
+                break;
+            } else if (p * p > i) {
+                Primes.push_back(i);
+                break;
+            }
+        }
+    }
+}
+
+fn prime_factors(usize n) -> vector<pair<usize, usize>> {
+    let factors = vector<pair<usize, usize>>();
+    for (let p: Primes) {
+        if (n == 1) {
+            break;
+        }
+        if (p * p > n) {
+            factors.push_back(pair(n, 1));
+            break;
+        }
+        let cnt = 0;
+        while (n % p == 0) {
+            n /= p;
+            cnt += 1;
+        }
+        if (cnt > 0) {
+            factors.push_back(pair(p, cnt));
+        }
+    }
+    return factors;
+}
+
+fn divisor_sum(usize n) -> usize {
+    static usize div_sum[N_MAX + 1];
+    if (div_sum[n] != 0) {
+        return div_sum[n];
+    }
+    let s = 1;
+
+    let fs = prime_factors(n);
+    for (let f: fs) {
+        s *= ((usize) pow(f.first, f.second + 1) - 1) / (f.first - 1);
+    }
+
+    div_sum[n] = s;
+    return s;
+}
+
+fn cumulative_divisor_sum(usize n) -> usize {
+    static usize cum_div_sum[N_MAX + 1];
+
+    if (cum_div_sum[n] != 0) {
+        return cum_div_sum[n];
+    }
+
+    for (usize i = 1; i <= N_MAX; i++) {
+        cum_div_sum[i] = divisor_sum(i) + cum_div_sum[i - 1];
+    }
+    return cum_div_sum[n];
+}
+
+fn main() -> int {
+    fastio();
+    generate_primes(N_MAX);
+    usize t;
+    cin >> t;
+    for (usize i = 0; i < t; i++) {
+        usize n;
+        cin >> n;
+        cout << cumulative_divisor_sum(n) << "\n";
+    }
+}