Problem:
Score : 300 points

Problem Statement

Given is a positive integer N.
How many tuples (A,B,C) of positive integers satisfy A \times B + C = N?

Constraints

2 \leq N \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

3

Sample Output 1

3

There are 3 tuples of integers that satisfy A \times B + C = 3: (A, B, C) = (1, 1, 2), (1, 2, 1), (2, 1, 1).

Sample Input 2

100

Sample Output 2

473

Sample Input 3

1000000

Sample Output 3

13969985

Solution in C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
#include <math.h>

int main(void){
    int N, pr, k, K, ans, tmp;
    scanf("%d", &N);

    ans = 0;

    for(int i=1; i<N; i++){
        tmp = 0;
        pr = N - i; // N-Cのこと
        // prをA*Bに分解
        K = sqrt(pr);
        for(k=1; k<=K; k++) if(pr%k == 0) tmp++;

        ans += (2*tmp);

        if(K*K == pr) ans--;
    }

    printf("%d\n", ans);

    return 0;
}