题意
设 $f(n)$ 为 $n=ab$ 的方案数，其中 $a,b$ 为无平方因子数。
例如，$f(6)=4$，因为 $6 = 1 imes 6 = 2 imes 3 = 3 imes 2 = 6 imes 1$，
$f(12)=2$，因为 $12 = 2 imes 6 = 6 imes 2$.
求 $displaystyle sum_{i=1}^nf(i)$，$n leq 2e7$，共有 $T$ 组询问（$T leq 20$）.
分析：
首先，$f(n)$ 可以在 $O(sqrt n)$ 的复杂度内算出来。
所以，可以分段打表，每隔一定间隔记录一个结果，然后在暴力查询。
假设间隔的 $size$ 为 $2500$，则共有 $8000$ 块，单次询问最坏复杂度为 $2500 imes sqrt 2e7 = 1e8$，
但实际复杂度很小，比标程还快很多。
#include<bits/stdc++.h> using namespace std; typedef long long ll; const int maxn = 2e7 + 10; const int siz = 2500; int n; ll f[maxn/siz + 10] = 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ll tongji(int n) { ll ret = 0; for(int i = 2;i *i <= n;i++) { int cnt = 0; while(n%i == 0) cnt++, n /= i; if(cnt == 1) ret++; if(cnt >= 3) return 0; //含有立方因子，答案为0 } if(n != 1) ret++; return 1<<ret; } int main() { int T; scanf("%d", &T); while(T--) { scanf("%d", &n); int t = n / siz; ll ans = f[t]; for(int i = t*siz+1;i <= n;i++) { ans += tongji(i); } printf("%lld ", ans); } return 0; }
参考链接：https://blog.csdn.net/wrwhahah/article/details/82423203