Aliquot sequence classifications: Difference between revisions

=={{header|AppleScript}}==

<lang applescript>on aliquotSum(n)

set sum to (n > 1) as integer

if (n > 1) then

set sqrt to n ^ 0.5

if (sqrt mod 1 is 0) then

set sum to sum + sqrt as integer

set sqrt to sqrt - 1

end if

repeat with i from (sqrt div 1) to 2 by -1

if (n mod i is 0) then set sum to sum + i + n div i

end repeat

end if

return sum

end aliquotSum

on aliquotSequence(k, maxLength, maxN)

-- Generate the sequence within the specified limitations.

set sequence to {k}

set n to k

repeat (maxLength - 1) times

set n to aliquotSum(n)

set repetition to (sequence contains n)

if (repetition) then exit repeat

set end of sequence to n

if ((n = 0) or (n > maxN)) then exit repeat

end repeat

-- Analyse it.

set sequenceLength to (count sequence)

if (sequenceLength is 1) then

set classification to "perfect"

else if (sequence ends with 0) then

set classification to "terminating"

else if (n = k) then

if (sequenceLength is 2) then

set classification to "amicable"

else

set classification to "sociable"

end if

else if (repetition) then

if (sequence ends with n) then

set classification to "aspiring"

else

set classification to "cyclic"

end if

else

set classification to "non-terminating"

end if

return {sequence:sequence, classification:classification}

end aliquotSequence

-- Task code:

local output, maxLength, maxN, spacing, astid, k

set output to {""}

set {maxLength, maxN} to {16, 2 ^ 47}

set spacing to " "

set astid to AppleScript's text item delimiters

set AppleScript's text item delimiters to ", "

repeat with k in {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ¬

11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488, 1.535571778608E+13}

set thisResult to aliquotSequence(k's contents, maxLength, maxN)

set end of output to text -18 thru -1 of (spacing & k) & ": " & ¬

text 1 thru 17 of (thisResult's classification & spacing) & thisResult's sequence

end repeat

set AppleScript's text item delimiters to linefeed

set output to output as text

set AppleScript's text item delimiters to astid

return output</lang>

{{output}}

<lang applescript>"

1: terminating 1, 0

2: terminating 2, 1, 0

3: terminating 3, 1, 0

4: terminating 4, 3, 1, 0

5: terminating 5, 1, 0

6: perfect 6

7: terminating 7, 1, 0

8: terminating 8, 7, 1, 0

9: terminating 9, 4, 3, 1, 0

10: terminating 10, 8, 7, 1, 0

11: terminating 11, 1, 0

12: terminating 12, 16, 15, 9, 4, 3, 1, 0

28: perfect 28

496: perfect 496

220: amicable 220, 284

1184: amicable 1184, 1210

12496: sociable 12496, 14288, 15472, 14536, 14264

1264460: sociable 1264460, 1547860, 1727636, 1305184

790: aspiring 790, 650, 652, 496

909: aspiring 909, 417, 143, 25, 6

562: cyclic 562, 284, 220

1064: cyclic 1064, 1336, 1184, 1210

1488: non-terminating 1488, 2480, 3472, 4464, 8432, 9424, 10416, 21328, 22320, 55056, 95728, 96720, 236592, 459792, 881392, 882384

1.535571778608E+13: non-terminating 1.535571778608E+13, 4.453466360112E+13, 1.449400874645E+14"</lang>