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47 lines
1.2 KiB
47 lines
1.2 KiB
#include <bits/stdc++.h>
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using namespace std;
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typedef long long LL;
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/**
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* 功能：线性筛出约数个数与约数和
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* Tag:模板，约数个数，约数和
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*/
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const int N = 1e6 + 10;
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int n;
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int primes[N]; //质数数组
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int idx; //质数数组下标游标
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bool st[N]; //是否已被筛出
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int d[N]; //约数个数数组
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int sigma[N]; //约数和数组
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void get_divisor(int n) {
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//积性函数的出发值
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d[1] = sigma[1] = 1;
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for (int i = 2; i <= n; i++) { //倍数
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if (!st[i])primes[++idx] = i, d[i] = 2, sigma[i] = i + 1;
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for (int j = 1; i * primes[j] <= n & j <= idx; j++) {
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st[i * primes[j]] = true;
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d[i * primes[j]] = d[i] << 1;
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sigma[i * primes[j]] = sigma[i] * (primes[j] + 1);
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if (i % primes[j] == 0) {
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d[i * primes[j]] -= d[i / primes[j]];
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sigma[i * primes[j]] -= primes[j] * sigma[i / primes[j]];
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break;
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}
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}
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}
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}
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LL res;
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int main() {
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cin >> n;
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//开始筛约数个数，约数和
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get_divisor(n);
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//输出约数个数和
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for (int i = 1; i <= n; i++) res += d[i];
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cout << res << endl;
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return 0;
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} |