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Template:Distinct prime factors
Please do not use this unfinished and/or still unreliable template.
Warning: All templates/parser functions nesting levels are used, so you can't nest it any further (e.g. you can't transclude the {{distinct prime factors/doc}} subpage) without causing deeply nested templates to fail to render, giving wrong results (prime factor greater than square root is missing for some numbers).
The {{distinct prime factors}} (or {{dpf}}) arithmetic function template returns a list of distinct prime factors of a nonzero integer, otherwise returns an error message.
Usage
[edit]- {{distinct prime factors|a nonzero integer|sep = list items separator (default , )}}
or
- {{distinct prime factors|a nonzero integer|list items separator (default , )}}
or
- {{dpf|a nonzero integer|sep = list items separator (default , )}}
or
- {{dpf|a nonzero integer|list items separator (default , )}}
where the sep default ,  gives , (comma followed by space.)
Valid input
[edit]A nonzero integer with absolute value less than 1031 2 = 1062961.
Examples
[edit]Examples with valid input (check primes with https://oeis.org/A000040/a000040.txt N. J. A. Sloane, Table of n, prime(n) for n = 1..100000)
Unfortunately, with the transclusion of {{Distinct prime factors/doc}} via the {{documentation}} template the precious limited nesting levels of templates and/or parser functions were exhausted! :-( Check {{Distinct prime factors/doc}} directly to see that all the tests are successful. Fortunately (not quite yet...), by transcluding {{Distinct prime factors/doc}} directly, borrowing the minimum code needed here from the {{documentation}} template, we manage to not exhaust the limit for most tests, but not for some of the largest numbers... :-( So you still have to check directly {{Distinct prime factors/doc}} to save some templates/parser functions nesting levels by avoiding the transclusion... You can see that all the tests are successful there.
Code Result {{dpf|210^2}} 2, 3, 5, 7 {{dpf|210^2|sep = ; }} 2; 3; 5; 7 {{dpf|210^2|sep =  * }} 2 * 3 * 5 * 7 {{dpf|210^2|sep =  + }} 2 + 3 + 5 + 7 {{dpf|-28}} 2, 7 {{dpf|-5}} 5 {{dpf|1}} {{dpf|7}} 7 {{dpf|15}} 3, 5 {{dpf|27}} 3 {{dpf|30}} 2, 3, 5 {{dpf|111}} 3, 37 {{dpf|5^3 * 11^2}} 5, 11 {{dpf|2^5 * 3^3 * 5}} 2, 3, 5 {{dpf|2^9 * 3^3}} 2, 3 {{dpf|37^2 + 8 * 37^2}} 3, 37 {{dpf|2^9 * (26 + 1)}} 2, 3 {{dpf|89 * 113}} 89, 113 {{dpf|79 * 79}} 79 {{dpf|210^2}} 2, 3, 5, 7 {{dpf|233^2}} 233 {{dpf|10000}} 2, 5 {{dpf|65535}} 3, 5, 17, 257 {{dpf|65536}} 2 {{dpf|65537}} 65537 {{dpf|65539}} 65539 {{dpf|65540}} 2, 5, 29, 113 {{dpf|65541}} 3, 7, 3121 {{dpf|65542}} 2, 32771 {{dpf|65543}} 65543 {{dpf|65547}} 3, 7283 {{dpf|65549}} 11, 59, 101 {{dpf|65551}} 65551 {{dpf|65553}} 3, 21851 {{dpf|65557}} 65557 {{dpf|65559}} 3, 13, 41 {{dpf|65561}} 53, 1237 {{dpf|65563}} 65563 {{dpf|65567}} 173, 379 {{dpf|65569}} 7, 17, 19, 29 {{dpf|65571}} 3, 11, 1987 {{dpf|65573}} 23, 2851 {{dpf|65577}} 3, 21859 {{dpf|65579}} 65579 {{dpf|265536}} 2, 3, 461 {{dpf|265537}} 131, 2027 {{dpf|265539}} 3, 88513 {{dpf|265541}} 265541 {{dpf|265543}} 265543 {{dpf|265547}} 265547 {{dpf|265549}} 37, 7177 {{dpf|265551}} 3, 11, 13, 619 {{dpf|265553}} 29, 9157 {{dpf|265557}} 3, 17, 41, 127 {{dpf|265559}} 7, 59, 643 {{dpf|265561}} 265561 {{dpf|265563}} 3, 19, 1553 {{dpf|265567}} 265567 {{dpf|265569}} 3, 88523 {{dpf|97 * 211}} 97, 211 {{dpf|216 * 211}} 2, 3, 211 {{dpf|1024 * 45}} 2, 3, 5 {{dpf|97 * 257}} 97, 257 {{dpf|3^6 * 5^2}} 3, 5 {{dpf|3 * 5^5}} 3, 5 {{dpf|17^2 * 191}} 17, 191 {{dpf|5 * 7 * 13 * 29}} 5, 7, 13, 29 {{dpf|5 * 7 * 13 * 29|sep = ; }} 5; 7; 13; 29 {{dpf|965536}} 2, 11, 13, 211 {{dpf|965537}} 67, 14411 {{dpf|965539}} 83, 11633 {{dpf|965541}} 3, 321847 {{dpf|965543}} 383, 2521 {{dpf|965547}} 3, 11, 3251 {{dpf|965549}} 13, 17, 257 {{dpf|965551}} 965551 {{dpf|965553}} 3, 321851 {{dpf|965557}} 31, 31147 {{dpf|965559}} 3, 7, 45979 {{dpf|965561}} 19, 89, 571 {{dpf|965563}} 23, 41981 {{dpf|965567}} 965567 {{dpf|965569}} 11, 61, 1439 {{dpf|997 * 1019}} 997, 1019 {{dpf|1015943}} 997, 1019
Examples with invalid input
code result {{dpf|0}} Distinct prime factors error: Argument must be a nonzero integer {{dpf|1031^2}} Distinct prime factors error: Argument must be a nonzero integer with absolute value < 1031 2 = 1062961
Formatted numbers
[edit]This template requires unformatted numbers, it will not recognize formatted numbers, e.g. comma separated, which is by design since formatted numbers will break expression parsers. To remove the formatting from a number, you can wrap the number first in {{formatnum:number|R}}.[1]
code result {{distinct prime factors|1,000}} Distinct prime factors error: Argument must be a nonzero integer {{distinct prime factors|{{formatnum:1,000|R}}}} 2, 5
Code
[edit]{{Distinct prime factors}} (or {{dpf}}) arithmetic function template
[edit]
<noinclude><!-- {{documentation}} --><!-- We can't use it here, the precious limited nesting levels of templates and/or parser functions get exhausted!
So we just borrow the necessary code from it instead.
--><div style="text-align: center; font-size: smaller;">The following [[Help:Documenting templates|documentation]] is located at [[Template:{{PAGENAME}}/doc]].</div>{{Template:{{PAGENAME}}/doc}}<!--
--></noinclude></noinclude><includeonly>{{ifint| {{{1|NAN}}}
| {{#ifexpr: ( ( abs ({{{1}}}) ) > 1 ) and ( ( abs ({{{1}}}) ) < 1031^2 )
| {{~dpf
| mpf = {{~mpf
| {{{1}}}
| mpf_le_sqrt(n) = {{mpf le sqrt(n)
| {{{1}}}
| sep = *
| key/val_sep = ^
}}
| sep = {{{sep|{{{2|, }}}}}}
| key/val_sep = ^
}}
| sep = {{{sep|{{{2|, }}}}}}
}}
| {{#ifexpr: ( abs ({{{1}}}) ) = 0
| {{error| Distinct prime factors error: Argument must be a nonzero integer }}
}}<!--
-->{{#ifexpr: ( abs ({{{1}}}) ) >= 1031^2
| {{error| Distinct prime factors error: Argument must be a nonzero integer with absolute value < 1031{{^|2}} {{=}} {{#expr: 1031^2 }} }}
}}
}}
| {{error| Distinct prime factors error: Argument must be a nonzero integer }}
}}</includeonly>
{{~Distinct prime factors}} (or {{~dpf}}) core function template
[edit]
{{#if: {{{mpf|}}}
| <!--
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 = 9699690
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 = 223092870
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 = 6469693230
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 * 31 = 200560490130
-->{{trim|<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|0}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|1}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|2}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|3}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|4}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|5}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|6}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|7}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|8}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{#explode:{{#explode:{{{mpf}}}|{{{sep|{{{2|, }}}}}}|9}}|^|0}}{{{sep|{{{2|, }}}}}}<!--
-->{{{sep|{{{2|, }}}}}}<!-- we need {{{sep|{{{2|, }}}}}} at least twice at the end for the {{trim}} template
-->|{{{sep|{{{2|, }}}}}}<!--
-->}}
| <!-- empty list: empty product of primes for the units (+/-)1, undefined prime factorization for 0 -->
}}
See also
[edit]
- {{distinct prime factors up to sqrt(n)}} or {{dpf le sqrt(n)}}
- {{distinct nontrivial prime factors}} or {{dpf lt n}}
- {{distinct prime factors}} or {{dpf}}
- {{number of distinct prime factors}} or {{little omega}}
- {{sum of distinct prime factors}} or {{sodpf}}
- {{product of distinct prime factors}} or {{squarefree kernel}} or {{radical}} or {{rad}}
- {{multiplicity}}
- {{prime factors (with multiplicity) up to sqrt(n)}} or {{mpf le sqrt(n)}}
- {{nontrivial prime factors (with multiplicity)}} or {{mpf lt n}}
- {{prime factors (with multiplicity)}} or {{mpf}} or {{factorization}}
- {{number of prime factors (with multiplicity)}} or {{big Omega}}
- {{sum of prime factors (with multiplicity)}} or {{sopfr}} or {{integer log}}
- {{product of prime factors (with multiplicity)}} (must give back {{abs|n}}, the absolute value of
)n
- {{quadratfrei}}
- {{Moebius mu}} or {{mu}}
- {{Euler phi}} or {{totient}}
- {{Dedekind psi}}
- {{number of divisors}} or {{sigma 0}} or {{tau}}
- {{sum of divisors}} or {{sigma 1}} or {{sigma}} (Cf. {{divisor function}} or {{sigma k}}, with
(default value))k = 1 - {{divisor function}} or {{sigma k}} (for
)k ≠ 0
External links
[edit]- Andrew Hodges, Java Applet for Factorization
- http://factordb.com/
