Difference between revisions of "Template:Divisor classes"

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imported>DSisyphBot
m (r2.5.1) (Robot: Adding eo, fr, sl, th)
imported>PrimeHunter
(Undid revision 954673663 by 87.95.193.244 (talk). No good reason for a red link here)
 
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{{Navbox
 
{{Navbox
|name       = Divisor classes navbox
+
| name = Divisor classes
|title     = Divisibility-based sets of integers
+
| state = {{{state|<includeonly>{{{1|collapsed}}}</includeonly>}}}
|image     = [[File:Lattice of the divisibility of 60.svg|200px|]]
+
| title = Divisibility-based sets of integers
|state      = collapsed
+
| image = [[File:Lattice of the divisibility of 60.svg|175px|Divisibility of 60]]
 +
| listclass = hlist
  
|group1   = Overview
+
| group1 = Overview
|list1     = [[Integer factorization]]{{·}} [[Divisor]]{{·}} [[Unitary divisor]]{{·}} [[Divisor function]]{{·}} [[Prime factor]]{{·}} [[Fundamental theorem of arithmetic]]
+
| list1 =
 +
* [[Integer factorization]]
 +
* [[Divisor]]
 +
* [[Unitary divisor]]
 +
* [[Divisor function]]
 +
* [[Prime factor]]
 +
* [[Fundamental theorem of arithmetic]]
  
|group2     = Forms of factorization
+
| group2 = Factorization forms
|list2     = [[Prime number]]{{·}} [[Composite number]]{{·}} [[Semiprime|Semiprime number]]{{·}} [[Pronic number]]{{·}} [[Sphenic number]]{{·}} [[Square-free integer|Square-free number]]{{·}} [[Powerful number]]{{·}} [[Perfect power]]{{·}} [[Achilles number]]{{·}} [[Smooth number]]{{·}} [[Regular number]]{{·}} [[Rough number]]{{·}} [[Unusual number]]
+
| list2 =
 +
* [[Prime number|Prime]]
 +
* [[Composite number|Composite]]
 +
* [[Semiprime]]
 +
* [[Pronic number|Pronic]]
 +
* [[Sphenic number|Sphenic]]
 +
* [[Square-free integer|Square-free]]
 +
* [[Powerful number|Powerful]]
 +
* [[Perfect power]]
 +
* [[Achilles number|Achilles]]
 +
* [[Smooth number|Smooth]]
 +
* [[Regular number|Regular]]
 +
* [[Rough number|Rough]]
 +
* [[Unusual number|Unusual]]
  
|group3     = Constrained divisor sums
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| group3 = Constrained divisor sums
|list3     = [[Perfect number]]{{·}} [[Almost perfect number]]{{·}} [[Quasiperfect number]]{{·}} [[Multiply perfect number]]{{·}} [[Hyperperfect number]]{{·}}  [[Superperfect number]]{{·}} [[Unitary perfect number]]{{·}} [[Semiperfect number]]{{·}} [[Primitive semiperfect number]]{{·}} [[Practical number]]
+
| list3 =
 +
* [[Perfect number|Perfect]]
 +
* [[Almost perfect number|Almost perfect]]
 +
* [[Quasiperfect number|Quasiperfect]]
 +
* [[Multiply perfect number|Multiply perfect]]
 +
* [[Hemiperfect number|Hemiperfect]]
 +
* [[Hyperperfect number|Hyperperfect]]
 +
* [[Superperfect number|Superperfect]]
 +
* [[Unitary perfect number|Unitary perfect]]
 +
* [[Semiperfect number|Semiperfect]]
 +
* [[Practical number|Practical]]
 +
* [[Erdős–Nicolas number|Erdős–Nicolas]]
  
|group4   = Numbers with many divisors
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| group4 = With many divisors
|list4     = [[Abundant number]]{{·}} [[Primitive abundant number]]{{·}} [[Highly abundant number]]{{·}} [[Superabundant number]]{{·}} [[Colossally abundant number]]{{·}} [[Highly composite number]]{{·}} [[Superior highly composite number]]{{·}} [[Weird number]]
+
| list4 =
 +
* [[Abundant number|Abundant]]
 +
* [[Primitive abundant number|Primitive abundant]]
 +
* [[Highly abundant number|Highly abundant]]
 +
* [[Superabundant number|Superabundant]]
 +
* [[Colossally abundant number|Colossally abundant]]
 +
* [[Highly composite number|Highly composite]]
 +
* [[Superior highly composite number|Superior highly composite]]
 +
* [[Weird number|Weird]]
  
|group5   = Numbers related<br/>to [[aliquot sequence]]s
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| group5 = [[Aliquot sequence]]-related
|list5     = [[Untouchable number]]{{·}} [[Amicable number]]{{·}} [[Sociable number]]
+
| list5 =
 +
* [[Untouchable number|Untouchable]]
 +
* [[Amicable numbers|Amicable]]
 +
* [[Sociable number|Sociable]]
 +
* [[Betrothed numbers|Betrothed]]
  
|group6   = Other
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| group6 = [[Radix|Base]]-dependent
|list6     = [[Deficient number]]{{·}} [[Friendly number]]{{·}} [[Friendly number#Solitary numbers|Solitary number]]{{·}} [[Sublime number]]{{·}} [[Harmonic divisor number]]{{·}} [[Frugal number]]{{·}} [[Equidigital number]]{{·}} [[Extravagant number]]
+
| list6 =
 +
* [[Equidigital number|Equidigital]]
 +
* [[Extravagant number|Extravagant]]
 +
* [[Frugal number|Frugal]]
 +
* [[Harshad number|Harshad]]
 +
* [[Polydivisible number|Polydivisible]]
 +
* [[Smith number|Smith]]
  
 +
| group7 = Other sets
 +
| list7 =
 +
* [[Arithmetic number|Arithmetic]]
 +
* [[Deficient number|Deficient]]
 +
* [[Friendly number|Friendly]]
 +
* [[Friendly number#Solitary numbers|Solitary]]
 +
* [[Sublime number|Sublime]]
 +
* [[Harmonic divisor number|Harmonic divisor]]
 +
* [[Descartes number|Descartes]]
 +
* [[Refactorable number|Refactorable]]
 +
* [[Superperfect number|Superperfect]]
 +
 +
}}<noinclude>
 +
{{documentation|content=
 +
 +
{{collapsible option |statename=optional |default=collapsed}}
 +
 +
==See also==
 +
*{{tl|Classes of natural numbers}}
 +
 +
[[Category:Mathematics navigational boxes]]
 
}}
 
}}
<noinclude>
 
[[Category:Mathematics templates|{{PAGENAME}}]]
 
[[eo:Ŝablono:Nombroj laŭ dividantoj]]
 
[[fr:Modèle:Palette Ensembles de divisibilité]]
 
[[sl:Predloga:Razredi deljivosti]]
 
[[th:แม่แบบ:ตัวหารจำนวนเต็ม]]
 
 
</noinclude>
 
</noinclude>

Latest revision as of 08:39, 19 December 2020

Template documentation

Initial visibility: currently defaults to collapsed

To set this template's initial visibility, the |state= parameter may be used:

  • |state=collapsed: {{Divisor classes|state=collapsed}} to show the template collapsed, i.e., hidden apart from its title bar
  • |state=expanded: {{Divisor classes|state=expanded}} to show the template expanded, i.e., fully visible
  • |state=autocollapse: {{Divisor classes|state=autocollapse}}
    • shows the template collapsed to the title bar if there is a {{navbar}}, a {{sidebar}}, or some other table on the page with the collapsible attribute
    • shows the template in its expanded state if there are no other collapsible items on the page

If the |state= parameter in the template on this page is not set, the template's initial visibility is taken from the |default= parameter in the Collapsible option template. For the template on this page, that currently evaluates to collapsed.

See also