Count intervals of size 1/n hit by the numbers 1/k; see https://math.stackexchange.com/questions/3664030.

Question3664030.java

public class Question3664030 {
    public static void main(String [] args) {
        for (int n = 1;n < 2000;n++) {
            int count = 0;
            boolean [] hit = new boolean [n];
            for (int k = 1;k <= n + 1;k++) {
                double x = 1. / k;
                // to count values on boundaries only towards the lower interval, subtract 1e-12 here ...
                int index = (int) (n * x);
                if (index < n && !hit [index]) {
                    hit [index] = true;
                    count++;
                }
                // ... and remove this second block.
                if (index == n * x && !hit [index - 1]) {
                    hit [index - 1] = true;
                    count++;
                }
            }
            System.out.println(n + " " + count);
        }
    }
}