100 cls
110 most = 1
120 maxcount = 0
130 print "The proper divisors of the following numbers are: ";chr$(10)
140 listproperdivisors(10)
150 for n = 2 to 20000
160 rem It is extremely slow in this loop
170   count = countproperdivisors(n)
180   if count > maxcount then
190     maxcount = count
200     most = n
210   endif
220 next n
230 print
240 print most;" has the most proper divisors, namely ";maxcount
250 end
260 function countproperdivisors(number)
270   if number < 2 then countproperdivisors = 0
280   count = 0
290   for i = 1 to int(number/2)
300     if number mod i = 0 then count = count+1
310   next i
320   countproperdivisors = count
330 end function
340 sub listproperdivisors(limit)
350   if limit < 1 then exit sub
360   for i = 1 to limit
370     print using "## ->";i;
380     if i = 1 then print " (None)";
390     for j = 1 to int(i/2)
400       if i mod j = 0 then print " ";j;
410     next j
420     print
430  next i
440 end sub