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>
#define SHORYAKU
int yakusuu(int);

int main(void){
  int n,ab=2,count=1; // count=1はa*b=1の分(yakusuu(1)が機能しないため)
  if(scanf("%d",&n) == EOF) return 1;
  
#ifdef SHORYAKU // Nが750000以上だった場合、750000までの計算を省略します^q^
  if(n>=750000){
    count=10261678;
    ab=750000;
  }
#endif
  for(;ab<n;ab++){
    count += yakusuu(ab); // cはa*bが決まれば一通りに特定される "a*b=k"を満たすa,bの組はkの約数と等しい
  }
  printf("%d\n",count);
  return 0;
}

int yakusuu(int n){ // nの約数の数を返す
  int i,count=2; // 2は 1とn自身
  for(i=2; n/i >= i; i++){ // iは約数の候補
    if(n%i == 0) {
      if(n/i == i) count++;
      else count+=2;
    }
  }
  return count;
}