Aliquot sequence classifications: Difference between revisions

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(Add C# implementation)
(→‎{{header|REXX}}: make it ooRexx compatible and readable)
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Both of the above limitations are imposed by this Rosetta Code task's restriction requirements:   ''For the purposes of this task, ···''.
Both of the above limitations are imposed by this Rosetta Code task's restriction requirements:   ''For the purposes of this task, ···''.
<syntaxhighlight lang="rexx">/*REXX program classifies various positive integers for types of aliquot sequences. */
<syntaxhighlight lang="rexx">/*REXX program classifies various positive integers For types of aliquot sequences.*/
parse arg low high $L /*obtain optional arguments from the CL*/
Parse Arg low high LL /*obtain optional arguments from the CL*/
high= word(high low 10,1); low= word(low 1,1) /*obtain the LOW and HIGH (range). */
high=word(high low 10,1)
low=word(low 1,1) /*obtain the LOW and HIGH (range). */
if $L='' then $L=11 12 28 496 220 1184 12496 1264460 790 909 562 1064 1488 15355717786080
If LL='' Then
numeric digits 100 /*be able to compute the number: BIG */
LL=11 12 28 496 220 1184 12496 1264460 790 909 562 1064 1488 15355717786080
big= 2**47; NTlimit= 16 + 1 /*limits for a non─terminating sequence*/
numeric digits max(9, length(big) ) /*be able to handle big numbers for // */
Numeric Digits 20 /*be able To compute the number: BIG */
big=2**47
digs= digits() /*used for align numbers for the output*/
#.= .; #.0= 0; #.1= 0 /*#. are the proper divisor sums. */
NTlimit=16+1 /*limit for a non-terminating sequence */
Numeric Digits max(9,length(big)) /*be able To handle big numbers For // */
say center('numbers from ' low " ───► " high ' (inclusive)', 153, "═")
do n=low to high; call classify n /*call a subroutine to classify number.*/
digs=digits() /*used For align numbers For the output*/
dsum.=.
end /*n*/ /* [↑] process a range of integers. */
dsum.0=0
say
dsum.1=0 /* dsum. are the proper divisor sums. */
say center('first numbers for each classification', 153, "═")
Say 'Numbers from ' low ' ---> ' high ' (inclusive):'
class.= 0 /* [↓] ensure one number of each class*/
do q=1 until class.sociable\==0 /*the only one that has to be counted. */
Do n=low To high /* process specified range */
call classify -q /*minus (-) sign indicates don't tell. */
Call classify n /* call subroutine To classify number. */
End
_= what; upper _ /*obtain the class and uppercase it. */
Say
class._= class._ + 1 /*bump counter for this class sequence.*/
Say 'First numbers for each classification:'
if class._==1 then say right(q, digs)':' center(what, digs) $
end /*q*/ /* [↑] only display the 1st occurrence*/
class.=0 /* [?] ensure one number of each class*/
say /* [↑] process until all classes found*/
Do q=1 Until class.sociable\==0 /*the only one that has To be counted. */
Call classify -q /*minus (-) sign indicates don't tell. */
say center('classifications for specific numbers', 153, "═")
do i=1 for words($L) /*$L: is a list of "special numbers".*/
_=translate(what) /*obtain the class and uppercase it. */
call classify word($L, i) /*call a subroutine to classify number.*/
class._=class._+1 /*bump counter For this class sequence.*/
end /*i*/ /* [↑] process a list of integers. */
If class._==1 Then /*first number of this class */
Call out q,what,dd
exit /*stick a fork in it, we're all done. */
End
/*──────────────────────────────────────────────────────────────────────────────────────*/
classify: parse arg a 1 aa; a= abs(a) /*obtain number that's to be classified*/
Say /* [?] process Until all classes found*/
Say 'Classifications for specific numbers:'
if #.a\==. then s= #.a /*Was this number been summed before?*/
else s= sigma(a) /*No, then classify number the hard way*/
Do i=1 To words(LL) /* process a list of "special numbers" */
#.a= s /*define sum of the proper divisors. */
Call classify word(LL,i) /*call subroutine To classify number. */
End
$= s /*define the start of integer sequence.*/
what= 'terminating' /*assume this kind of classification. */
Exit /*stick a fork in it,we're all done. */
out:
c.= 0 /*clear all cyclic sequences (to zero).*/
Parse arg number,class,dd
c.s= 1 /*set the first cyclic sequence. */
dd.=''
if $==a then what= 'perfect' /*check for a "perfect" number. */
Do di=1 By 1 While length(dd)>50
else do t=1 while s>0 /*loop until sum isn't 0 or > big.*/
do dj=50 To 10 By -1
m= s /*obtain the last number in sequence. */
If substr(dd,dj,1)=' ' Then Leave
if #.m==. then s= sigma(m) /*Not defined? Then sum proper divisors*/
End
else s= #.m /*use the previously found integer. */
dd.di=left(dd,dj)
if m==s then if m>=0 then do; what= 'aspiring'; leave; end
dd=substr(dd,dj+1)
parse var $ . word2 . /*obtain the 2nd number in sequence. */
End
if word2==a then do; what= 'amicable'; leave; end
dd.di=dd
$= $ s /*append a sum to the integer sequence.*/
Say right(number,digs)':' center(class,digs) dd.1||conti(1)
if s==a then if t>3 then do; what= 'sociable'; leave; end
Do di=2 By 1 While dd.di>''
if c.s then if m>0 then do; what= 'cyclic' ; leave; end
Say copies(' ',33)dd.di||conti(di)
c.s= 1 /*assign another possible cyclic number*/
End
/* [↓] Rosetta Code task's limit: >16 */
Return
if t>NTlimit then do; what= 'non─terminating'; leave; end
conti:
if s>big then do; what= 'NON─TERMINATING'; leave; end
Parse arg this
end /*t*/ /* [↑] only permit within reason. */
next=this+1
if aa>0 then say right(a, digs)':' center(what, digs) $
If dd.next>'' Then Return '...'
return /* [↑] only display if AA is positive*/
Else Return ''
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*---------------------------------------------------------------------------------*/
sigma: procedure expose #. !.; parse arg x; if 11<2 then return 0; odd= x // 2
classify:
s= 1 /* [↓] use EVEN or ODD integers. ___*/
Parse Arg a 1 aa
do j=2+odd by 1+odd while j*j<x /*divide by all the integers up to √ X */
if x//j==0 then s= s + j + x % j /*add the two divisors to the sum. */
a=abs(a) /*obtain number that's to be classified*/
If dsum.a\==. Then
end /*j*/ /* [↓] adjust for square. ___*/
if j*j==x then s= s + j /*Was X a square? If so, add √ X */
s=dsum.a /*Was this number been summed before?*/
Else
#.x= s /*memoize division sum for argument X.*/
return s /*return " " " " " */</syntaxhighlight>
s=dsum(a) /*No,Then classify number the hard way */
dsum.a=s /*define sum of the proper divisors. */
dd=s /*define the start of integer sequence.*/
what='terminating' /*assume this kind of classification. */
c.=0 /*clear all cyclic sequences (to zero).*/
c.s=1 /*set the first cyclic sequence. */
If dd==a Then
what='perfect' /*check For a "perfect" number. */
Else Do t=1 By 1 While s>0 /*loop Until sum isn't 0 or > big.*/
m=s /*obtain the last number in sequence. */
If dsum.m==. Then /*Not defined? */
s=dsum(m) /* compute sum pro of per divisors */
Else
s=dsum.m /*use the previously found integer. */
If m==s Then
If m>=0 Then Do
what='aspiring'
Leave
End
If word(dd,2)=a Then Do
what='amicable'
Leave
End
dd=dd s /*append a sum To the integer sequence.*/
If s==a Then
If t>3 Then Do
what='sociable'
Leave
End
If c.s Then
If m>0 Then Do
what='cyclic'
Leave
End
c.s=1 /*assign another possible cyclic number*/
/* [?] Rosetta Code task's limit: >16 */
If t>NTlimit Then Do
what='non-terminating'
Leave
End
If s>big Then Do
what='NON-TERMINATING'
Leave
End
End
If aa>0 Then /* display only if AA is positive */
Call out a,what,dd
Return
/*---------------------------------------------------------------------------------*/
dsum: Procedure Expose dsum. /* compute the sum of proper divisors */
Parse Arg x
If x<2 Then
Return 0
odd=x//2
s=1 /* use EVEN or ODD integers. */
Do j=2+odd by 1+odd While j*j<x /* divide by all the integers ) */
/* up to but excluding sqrt(x) */
If x//j==0 Then /* j is a divisor, so is x%j */
s=s+j+x%j /*add the two divisors To the sum. */
End
If j*j==x Then /* if x is a square */
s=s+j /* add sqrt(X) */
dsum.x=s /* memoize proper divisor sum of X */
Return s /* return the proper divisor sum */
</syntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
{{out|output|text=&nbsp; when using the default input:}}
<pre>Numbers from 1 ---> 10 (inclusive):
(Shown at three-quarter size.)

<pre style="font-size:75%">
═════════════════════════════════════════════════════════numbers from 1 ───► 10 (inclusive)══════════════════════════════════════════════════════════
1: terminating 0
1: terminating 0
2: terminating 1 0
2: terminating 1 0
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10: terminating 8 7 1 0
10: terminating 8 7 1 0


First numbers for each classification:
══════════════════════════════════════════════════════════first numbers for each classification══════════════════════════════════════════════════════════
1: terminating 0
1: terminating 0
6: perfect 6
6: perfect 6
25: aspiring 6
25: aspiring 6
138: non─terminating 150 222 234 312 528 960 2088 3762 5598 6570 10746 13254 13830 19434 20886 21606 25098 26742 26754
138: non-terminating 150 222 234 312 528 960 2088 3762 5598 6570 10746 ...
13254 13830 19434 20886 21606 25098 26742 26754
220: amicable 284 220
220: amicable 284 220
562: cyclic 284 220 284
562: cyclic 284 220 284
12496: sociable 14288 15472 14536 14264 12496
12496: sociable 14288 15472 14536 14264 12496


Classifications for specific numbers:
══════════════════════════════════════════════════════════classifications for specific numbers═══════════════════════════════════════════════════════════
11: terminating 1 0
11: terminating 1 0
12: terminating 16 15 9 4 3 1 0
12: terminating 16 15 9 4 3 1 0
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562: cyclic 284 220 284
562: cyclic 284 220 284
1064: cyclic 1336 1184 1210 1184
1064: cyclic 1336 1184 1210 1184
1488: non─terminating 2480 3472 4464 8432 9424 10416 21328 22320 55056 95728 96720 236592 459792 881392 882384 1474608 2461648 3172912 3173904
1488: non-terminating 2480 3472 4464 8432 9424 10416 21328 22320 55056 ...
95728 96720 236592 459792 881392 882384 1474608 ...
15355717786080: NON─TERMINATING 44534663601120 144940087464480
2461648 3172912 3173904
15355717786080: NON-TERMINATING 44534663601120 144940087464480

</pre>
</pre>


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