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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.
Contents
Usage
- {{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
A nonzero integer with absolute value less than 1031 2 = 1062961.
Examples
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 {{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 {{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 {{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 {{dpf|1015943}} 997
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
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
{{Distinct prime factors}} (or {{dpf}}) arithmetic function template
<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
{{#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
- {{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
- Andrew Hodges, Java Applet for Factorization
- http://factordb.com/
