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;
  scanf("%d", &n);
  int c, count=0, tmpcount, i, q;
  for(c=1; c<n; c++) {
    tmpcount=0;
    // 1..sqrt(n-c)でn-cを割り，余り0ならば割り切れる
    q = (int)sqrt(n-c);
    //printf("%d\n", q);
    // n-cをa*bにした時の(a,b)の数
    for(i=1; i<=q; i++) {
      //printf("%d, %d\n", n-c, i);
      if((n-c) % i == 0) {
        //printf("fuck\n");
        tmpcount++;
      }
    }
    // n-cが平方数でなければtmpcountの2倍，
    // 平方数ならば2倍から1引く
    if(q*q != (n-c)) {
      count += (tmpcount*2);
    }
    else {
      count += (tmpcount*2 - 1);
    }
  }
  printf("%d\n", count);
  return 0;
}