Proper Divisor mash-up
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)