题意

\(求\Sigma \lfloor \frac{n}{i} \rfloor\)

Input starts with an integer T (≤ 1000), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n < 2^31).

Sol

数论分块

# include <bits/stdc++.h>

# define RG register

# define IL inline

# define Fill(a, b) memset(a, b, sizeof(a))

using namespace std;

typedef long long ll;

IL ll Read(){

	char c = '%'; ll x = 0, z = 1;

	for(; c > '9' || c < '0'; c = getchar()) if(c == '-') z = -1;

	for(; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - '0';

	return x * z;

}

ll n, ans;

int main(RG int argc, RG char *argv[]){

	for(RG int T = Read(), Case = 1; Case <= T; ++Case){

		n = Read(); ans = 0;

		for(RG ll i = 1, j; i <= n; i = j + 1){

			j = min(n, n / (n / i));

			ans += 1LL * (n / i) * (j - i + 1);

		}

		printf("Case %d: %lld\n", Case, ans);

	}

	return 0;

}