Anti-primes: Difference between revisions
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(→version 1: changed the format of the output from horizontal to vertical.) |
m (→{{header|REXX}}: elided REXX version 2.) |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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===version 1=== |
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This REXX version is using a modified version of a highly optimized ''proper divisors'' function. |
This REXX version is using a modified version of a highly optimized ''proper divisors'' function. |
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Programming note: although the solution to this Rosetta Code task is trivial, a fair amount of optimization was incorporated into the REXX program to find larger anti─primes (highly─composite numbers). |
Programming note: although the solution to this Rosetta Code task is trivial, a fair amount of optimization was incorporated into the REXX program to find larger anti─primes (highly─composite numbers). |
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The #DIVS function could be further optimized by only processing ''even'' numbers, with unity being treated as a special case. |
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<lang rexx>/*REXX program finds N number of anti─primes or highly─composite numbers. */ |
<lang rexx>/*REXX program finds N number of anti─primes or highly─composite numbers. */ |
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parse arg N . /*obtain optional argument from the CL.*/ |
parse arg N . /*obtain optional argument from the CL.*/ |
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</pre> |
</pre> |
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===version 2=== |
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This REXX version takes advantage of the fact that anti─primes (highly─composite numbers) above 59 can be incremented by 20. |
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<lang rexx>/*REXX program finds N number of anti─primes or highly─composite numbers. */ |
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parse arg N . /*obtain optional argument from the CL.*/ |
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if N=='' | N=="," then N=55 /*Not specified? Then use the default.*/ |
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maxD= 0 /*the maximum number of divisors so far*/ |
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#= 0 /*the count of anti─primes found " " */ |
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$= /*the list of anti─primes found " " */ |
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do j=1 for 59 while #<N /*step through possible numbers by twos*/ |
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d= #divs(j) /*obtain the number of divisors for K.*/ |
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if d<=maxD then iterate /*Is D ≤ previous div count? Skip it. */ |
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#= # + 1; $= $ j /*found an anti─prime #, add it to list*/ |
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say right(#, 11) j |
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maxD= d /*use this as the new high─water mark. */ |
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end /*j*/ |
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do j=60 by 20 while #<N /*step through possible numbers by 20. */ |
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d= #divs(j) /*obtain the number of divisors for K.*/ |
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if d<=maxD then iterate /*Is D ≤ previous div count? Skip it. */ |
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#= # + 1; $= $ j /*found an anti─prime #, add it to list*/ |
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say right(#, 11) j |
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maxD= d /*use this as the new high─water mark. */ |
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end /*j*/ |
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exit /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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#divs: procedure; parse arg x 1 y /*X and Y: both set from 1st argument.*/ |
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if x<3 then return x /*handle special case for one and two. */ |
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if x==4 then return 3 /* " " " " four. */ |
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if x<6 then return 2 /* " " " " three or five*/ |
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odd= x // 2 /*check if X is odd or not. */ |
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if odd then do; #= 1; end /*Odd? Assume Pdivisors count of 1.*/ |
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else do; #= 3; y= x%2; end /*Even? " " " " 3.*/ |
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/* [↑] start with known num of Pdivs.*/ |
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do k=3 for x%2-3 by 1+odd while k<y /*for odd numbers, skip evens.*/ |
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if x//k==0 then do /*if no remainder, then found a divisor*/ |
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#=#+2; y=x%k /*bump # Pdivs, calculate limit Y. */ |
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if k>=y then do; #= #-1; leave; end /*limit?*/ |
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end /* ___ */ |
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else if k*k>x then leave /*only divide up to √ x */ |
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end /*k*/ /* [↑] this form of DO loop is faster.*/ |
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return #+1 /*bump "proper divisors" to "divisors".*/</lang> |
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{{out|output|text= when using the default input of: <tt> 55 </tt>}} |
{{out|output|text= when using the default input of: <tt> 55 </tt>}} |
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<pre> |
<pre> |
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─index─ ──anti─prime── |
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1 1 |
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1 1 |
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2 2 |
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3 4 |
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4 6 |
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5 12 |
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6 24 |
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7 36 |
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8 48 |
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9 60 |
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10 120 |
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11 180 |
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12 240 |
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13 360 |
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14 720 |
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15 840 |
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16 1260 |
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17 1680 |
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18 2520 |
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19 5040 |
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20 7560 |
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21 10080 |
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22 15120 |
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23 20160 |
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24 25200 |
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25 27720 |
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26 45360 |
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27 50400 |
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28 55440 |
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29 83160 |
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30 110880 |
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31 166320 |
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32 221760 |
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33 277200 |
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34 332640 |
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35 498960 |
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36 554400 |
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37 665280 |
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38 720720 |
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39 1081080 |
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40 1441440 |
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41 2162160 |
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42 2882880 |
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43 3603600 |
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44 4324320 |
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45 6486480 |
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46 7207200 |
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47 8648640 |
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48 10810800 |
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49 14414400 |
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50 17297280 |
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51 21621600 |
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52 32432400 |
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53 36756720 |
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54 43243200 |
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55 61261200 |
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</pre> |
</pre> |
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