The   proper divisors   of a positive integer N are those numbers, other than N itself, that divide N without remainder.

For N > 1 they will always include 1,   but for N == 1 there are no proper divisors.



Examples

The proper divisors of     6     are   1, 2, and 3.

The proper divisors of   100   are   1, 2, 4, 5, 10, 20, 25, and 50.



Task

 Create a routine to generate all the proper divisors of a number.
 use it to show the proper divisors of the numbers 1 to 10 inclusive.
 Find a number in the range 1 to 20,000 with the most proper divisors. Show the number and just the count of how many proper divisors it has.


Show all output here.



Related tasks

   Amicable pairs
   Abundant, deficient and perfect number classifications
   Aliquot sequence classifications
   Factors of an integer
   Prime decomposition


 
 
      function icntprop(num  )
      icnt=0
      do i=1 , num-1
          if (mod(num , i)  .eq. 0)  then
          icnt = icnt + 1
          if (num .lt. 11) print *,'    ',i
          end if
          end do
      icntprop =  icnt
      end function
 
      limit = 20000
      maxcnt = 0
      print *,'N   divisors'
      do j=1,limit,1
      if (j .lt. 11) print *,j
      icnt = icntprop(j)
 
      if (icnt .gt. maxcnt) then
      maxcnt = icnt
      maxj = j
      end if
 
      end do
 
      print *,' '
      print *,' from 1 to ',limit
      print *,maxj,' has max proper divisors: ',maxcnt
      end
 