How to resolve the algorithm Aliquot sequence classifications step by step in the J programming language

Published on 12 May 2024 09:40 PM
#J

How to resolve the algorithm Aliquot sequence classifications step by step in the J programming language

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Problem Statement

An aliquot sequence of a positive integer K is defined recursively as the first member being K and subsequent members being the sum of the Proper divisors of the previous term.

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Step by Step solution about How to resolve the algorithm Aliquot sequence classifications step by step in the J programming language

Source code in the j programming language

proper_divisors=: [: */@>@}:@,@{ [: (^ i.@>:)&.>/ 2 p: x:
aliquot=: +/@proper_divisors ::0:
rc_aliquot_sequence=: aliquot^:(i.16)&>
rc_classify=: 3 :0
      if. 16 ~:# y                 do. ' invalid        '
  elseif. 6 > {: y                 do. ' terminate      '
  elseif. (+./y>2^47) +. 16 = #~.y do. ' non-terminating'
  elseif. 1=#~. y                  do. ' perfect        '
  elseif. 8= st=. {.#/.~ y         do. ' amicable       '
  elseif. 1 < st                   do. ' sociable       '
  elseif. =/_2{. y                 do. ' aspiring       '
  elseif. 1                        do. ' cyclic         '
  end.
)
rc_display_aliquot_sequence=: (rc_classify,' ',":)@:rc_aliquot_sequence


   rc_display_aliquot_sequence&> >: i.10
 terminate       1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 terminate       2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 terminate       3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 terminate       4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
 terminate       5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 perfect         6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 
 terminate       7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 terminate       8 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
 terminate       9 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 
 terminate       10 8 7 1 0 0 0 0 0 0 0 0 0 0 0 0

   rc_display_aliquot_sequence&>11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488, 15355717786080x
 terminate       11 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 terminate       12 16 15 9 4 3 1 0 0 0 0 0 0 0 0 0
 perfect         28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28
 perfect         496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496
 amicable        220 284 220 284 220 284 220 284 220 284 220 284 220 284 220 284
 amicable        1184 1210 1184 1210 1184 1210 1184 1210 1184 1210 1184 1210 1184 1210 1184 1210
 sociable        12496 14288 15472 14536 14264 12496 14288 15472 14536 14264 12496 14288 15472 14536 14264 12496
 sociable        1264460 1547860 1727636 1305184 1264460 1547860 1727636 1305184 1264460 1547860 1727636 1305184 1264460 1547860 1727636 1305184
 aspiring        790 650 652 496 496 496 496 496 496 496 496 496 496 496 496 496
 aspiring        909 417 143 25 6 6 6 6 6 6 6 6 6 6 6 6
 cyclic          562 284 220 284 220 284 220 284 220 284 220 284 220 284 220 284
 cyclic          1064 1336 1184 1210 1184 1210 1184 1210 1184 1210 1184 1210 1184 1210 1184 1210
 non-terminating 1488 2480 3472 4464 8432 9424 10416 21328 22320 55056 95728 96720 236592 459792 881392 882384
 non-terminating 15355717786080 44534663601120 144940087464480 471714103310688 1130798979186912 2688948041357088 6050151708497568 13613157922639968 35513546724070632 74727605255142168 162658586225561832 353930992506879768 642678347124409032 1125102611548462968 1977286128289819992 3415126495450394808

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