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 PHP (7.4.4) (judge verdict: Accepted)

<?php
$n = fgets(STDIN);

//$a*$b+$c=$n;
$count=0;
/*
for($c=1;$c<=$n-2;$c++){
    for($b=1;$b<=$n-2;$b++) {
        if( ($n-$c)%$b == 0){
            $count++;
        }
        if($n-$c < $b){
            break;
        }
    }
}
print $count;
*/
$amax = sqrt($n);
for($a=1;$a<$amax;$a++) {
    $bmax = $n/$a;
    for ($b = $a; $b < $bmax; $b++) {
        //print($n - $a*$b . "\n");
        if($a == $b){
            $result += 1;
        } else {
            $result += 2;
        }

    }
}
print $result;
?>