OPENW 1
CLEARW 1
'
' Array f% is used to hold the divisors
DIM f%(SQR(20000)) ! cannot redim arrays, so set size to largest needed
'
' 1. Show proper divisors of 1 to 10, inclusive
'
FOR i%=1 TO 10
  num%=@proper_divisors(i%)
  PRINT "Divisors for ";i%;":";
  FOR j%=1 TO num%
    PRINT " ";f%(j%);
  NEXT j%
  PRINT
NEXT i%
'
' 2. Find (smallest) number <= 20000 with largest number of proper divisors
'
result%=1 ! largest so far
number%=0 ! its number of divisors
FOR i%=1 TO 20000
  num%=@proper_divisors(i%)
  IF num%>number%
    result%=i%
    number%=num%
  ENDIF
NEXT i%
PRINT "Largest number of divisors is ";number%;" for ";result%
'
~INP(2)
CLOSEW 1
'
' find the proper divisors of n%, placing results in f%
' and return the number found
'
FUNCTION proper_divisors(n%)
  LOCAL i%,root%,count%
  '
  ARRAYFILL f%(),0
  count%=1 ! index of next slot in f% to fill
  '
  IF n%>1
    f%(count%)=1
    count%=count%+1
    root%=SQR(n%)
    FOR i%=2 TO root%
      IF n% MOD i%=0
        f%(count%)=i%
        count%=count%+1
        IF i%*i%<>n% ! root% is an integer, so check if i% is actual squa- lists:seq(1,10)].
X: 1, N: []
X: 2, N: [1]
X: 3, N: [1]
X: 4, N: [1,2]
X: 5, N: [1]
X: 6, N: [1,2,3]
X: 7, N: [1]
X: 8, N: [1,2,4]
X: 9, N: [1,3]
X: 10, N: [1,2,5]
[ok,ok,ok,ok,ok,ok,ok,ok,ok,ok]

2> properdivs:longest(20000).
With 79, Number 15120 has the most divisors
re root of n%
          f%(count%)=n%/i%
          count%=count%+1
        ENDIF
      ENDIF
    NEXT i%
  ENDIF
  '
  RETURN count%-1
ENDFUNC