Proper Divisor mash-up A proper divisor is a divisor of a number n, which is not n itself. For example, the proper divisors of 12 are 1, 2, 3, 4 and 6.
You will be given an integer x, x ≥ 2, x ≤ 1000. Your task is to sum all the highest proper divisors of the integers from 2 to x (inclusive) (OEIS A280050).
Example (with x = 6):

Find all the integers between 2 and 6 (inclusive): 2,3,4,5,6.

Get the proper divisors of all of them, and pick the highest ones from each number:

2 -&gt; 1
3 -&gt; 1
4 -&gt; 1, 2
5 -&gt; 1
6 -&gt; 1, 2, 3.


Sum the highest proper divisors: 1 + 1 + 2 + 1 + 3 = 8.

The final result is 8.


Test Cases

Input  |  Output
-------+---------
       |
 2     | 1
 4     | 4
 6     | 8
 8     | 13
 15    | 41
 37    | 229
 100   | 1690
 1000  | 165279

Rules

Default Loopholes apply.

You can take input and provide output by any standard method.

This is code-golf, the shortest valid submission in each language wins! Have Fun!
Oasis, 4 bytes
Code:
nj+U

Try it online!
Explanation:
Extended version:
nj+00

    0   = a(0)
   0    = a(1)

a(n) =

n       # Push n
 j      # Get the largest divisor under n
  +     # Add to a(n - 1)