Template:Product of distinct prime factors

The following documentation is located at Template:Product of distinct prime factors/doc.

The {{product of distinct prime factors}} arithmetic function template returns the product of distinct prime factors of n (squarefree kernel of n) (radical of n, rad(n)) of a nonzero integer, otherwise returns an error message.

Usage

{{product of distinct prime factors|a nonzero integer}}

or

{{squarefree kernel|a nonzero integer}}

or

{{radical|a nonzero integer}}

or

{{rad|a nonzero integer}}

Valid input

A nonzero integer less than 1031 2 = 1062961 (validation is done by the {{mpf}} arithmetic function template).

Examples

Examples with valid input (check with https://oeis.org/A007947/b007947.txt Table of n, rad(n) for n = 1..100000)

Unfortunately, with the transclusion of {{product of distinct prime factors/doc}} via the {{documentation}} template the precious limited nesting levels of templates and/or parser functions were exhausted! :-( Check {{product of distinct prime factors/doc}} directly to see that all the tests are successful. Fortunately, by transcluding {{product of distinct prime factors/doc}} directly, borrowing the minimum code needed here from the {{documentation}} template, we manage to not exhaust the limit! :-)

Code	Result	Comment
{{product of distinct prime factors|210^2}}	210
{{squarefree kernel|210^2}}	210
{{radical|210^2}}	210
{{rad|210^2}}	210
{{rad|-28}}	14
{{rad|-5}}	5
{{rad|-1}}	1	(empty product, i.e 1)
{{rad|1}}	1	(empty product, i.e 1)
{{rad|7}}	7
{{rad|15}}	15
{{rad|27}}	3
{{rad|30}}	30
{{rad|111}}	111
{{rad|5^3 * 11^2}}	55
{{rad|2^5 * 3^3 * 5}}	30
{{rad|2^9 * 3^3}}	6
{{rad|37^2 + 8 * 37^2}}	111
{{rad|2^9 * (26 + 1)}}	6
{{rad|89 * 113}}	10057
{{rad|79 * 79}}	79
{{rad|210^2}}	210
{{rad|233^2}}	233
{{rad|10000}}	10
{{rad|65535}}	65535
{{rad|65536}}	2
{{rad|65537}}	65537
{{rad|65539}}	65539
{{rad|65540}}	32770
{{rad|65541}}	65541
{{rad|65542}}	65542
{{rad|65543}}	65543
{{rad|65547}}	21849
{{rad|65549}}	65549
{{rad|65551}}	65551
{{rad|65553}}	65553
{{rad|65557}}	65557
{{rad|65559}}	1599
{{rad|65561}}	65561
{{rad|65563}}	65563
{{rad|65567}}	65567
{{rad|65569}}	65569
{{rad|65571}}	65571
{{rad|65573}}	65573
{{rad|65577}}	65577
{{rad|65579}}	65579
{{rad|265535}}	265535
{{rad|265536}}	2766
{{rad|265537}}	265537
{{rad|265539}}	265539
{{rad|265540}}	132770
{{rad|265541}}	265541
{{rad|265542}}	265542
{{rad|265543}}	265543
{{rad|265547}}	265547
{{rad|265549}}	265549
{{rad|265551}}	265551
{{rad|265553}}	265553
{{rad|265557}}	265557
{{rad|265559}}	265559
{{rad|265561}}	265561
{{rad|265563}}	88521
{{rad|265567}}	265567
{{rad|265569}}	265569
{{rad|265571}}	265571
{{rad|265573}}	265573
{{rad|265577}}	265577
{{rad|265579}}	265579
{{rad|257}}	257
{{rad|97 * 211}}	20467
{{rad|216 * 211}}	1266
{{rad|1024 * 45}}	30
{{rad|97 * 257}}	24929
{{rad|3^6 * 5^2}}	15
{{rad|3 * 5^5}}	15
{{rad|17^2 * 191}}	3247
{{rad|5 * 7 * 13 * 29}}	13195
{{rad|509^2}}	509
{{rad|965535}}	965535
{{rad|965536}}	60346
{{rad|965537}}	965537
{{rad|965539}}	965539
{{rad|965540}}	482770
{{rad|965541}}	965541
{{rad|965542}}	965542
{{rad|965543}}	965543
{{rad|965547}}	107283
{{rad|965549}}	56797
{{rad|965551}}	965551
{{rad|965553}}	965553
{{rad|965557}}	965557
{{rad|965559}}	965559
{{rad|965561}}	965561
{{rad|965563}}	965563
{{rad|965567}}	965567
{{rad|965569}}	965569
{{rad|965571}}	965571
{{rad|965573}}	965573
{{rad|965577}}	965577
{{rad|965579}}	965579
{{rad|1015941}}	1015941
{{rad|997 * 1019}}	1015943
{{rad|1015943}}	1015943
{{rad|1015945}}	1015945
{{rad|1015947}}	338649
{{rad|1015949}}	1015949
{{rad|1015950}}	203190

Examples with invalid input (argument validation by {{rad}} is omitted to spare some precious limited nesting levels of templates and/or parser functions).

Code	Result
{{rad|0}}
{{rad|1031^2}}

Code

<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><includeonly>{{#expr: 0{{mpf| {{{1|1}}} |sep = * |key/val_sep = * 1^}} + {{#ifexpr: abs ({{{1|1}}}) = 1 | 1 | 0 }} }}</includeonly>

See also

• {{if prime}} or {{is prime}}

• {{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

  k = 1

  (default value))
• {{divisor function}} or {{sigma k}} (for

  k   ≠   0

  )

External links

• Andrew Hodges, Java Applet for Factorization
• http://factordb.com/