These define three classifications of positive integers based on their   proper divisors.

Let   P(n)   be the sum of the proper divisors of   n   where the proper divisors are all positive divisors of   n   other than   n   itself.

   if    P(n) <  n    then  n  is classed as  deficient  (OEIS A005100).
   if    P(n) == n    then  n  is classed as  perfect    (OEIS A000396).
   if    P(n) >  n    then  n  is classed as  abundant   (OEIS A005101).



Example

6   has proper divisors of   1,   2,   and   3.

1 + 2 + 3 = 6,   so   6   is classed as a perfect number.



Task

Calculate how many of the integers   1   to   20,000   (inclusive) are in each of the three classes.

Show the results here.



Related tasks

   Aliquot sequence classifications.   (The whole series from which this task is a subset.)
   Proper divisors
   Amicable pairs


 
@echo off
setlocal enabledelayedexpansion
 
:_main
 
for /l %%i in (1,1,20000) do (
 
  echo Processing %%i
 
  call:_P %%i
  set Pn=!errorlevel!
  if !Pn! lss %%i set /a deficient+=1
  if !Pn!==%%i set /a perfect+=1
  if !Pn! gtr %%i set /a abundant+=1
  cls
)
 
echo Deficient - %deficient% ^| Perfect - %perfect% ^| Abundant - %abundant%
pause>nul
 
 
:_P
setlocal enabledelayedexpansion
set sumdivisers=0
 
set /a upperlimit=%1-1
 
for /l %%i in (1,1,%upperlimit%) do (
  set /a isdiviser=%1 %% %%i
  if !isdiviser!==0 set /a sumdivisers+=%%i
)
 
exit /b %sumdivisers%
 