Difference between revisions of "Template:Divisor classes"

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imported>PrimeHunter
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{{Navbox
 
{{Navbox
|name = Divisor classes navbox
+
| name = Divisor classes
|state = collapsed
+
| state = {{{state|<includeonly>{{{1|collapsed}}}</includeonly>}}}
|title = Divisibility-based sets of integers
+
| title = Divisibility-based sets of integers
|image = [[File:Lattice of the divisibility of 60.svg|200px|Divisibility of 60]]
+
| image = [[File:Lattice of the divisibility of 60.svg|175px|Divisibility of 60]]
 +
| listclass = hlist
  
|group1 = Overview
+
| group1 = Overview
|list1 = {{nowrap begin}}
+
| list1 =
[[Integer factorization]]{{·w}}[[Divisor]]{{·w}}[[Unitary divisor]]{{·w}}[[Divisor function]]{{·w}}[[Prime factor]]{{·w}}[[Fundamental theorem of arithmetic]]
+
* [[Integer factorization]]
{{nowrap end}}
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* [[Divisor]]
 +
* [[Unitary divisor]]
 +
* [[Divisor function]]
 +
* [[Prime factor]]
 +
* [[Fundamental theorem of arithmetic]]
  
|group2 = Forms of factorization
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| group2 = Factorization forms
|list2 = {{nowrap begin}}
+
| list2 =
[[Prime number]]{{·w}}[[Composite number]]{{·w}}[[Semiprime|Semiprime number]]{{·w}}[[Pronic number]]{{·w}}[[Sphenic number]]{{·w}}[[Square-free integer|Square-free number]]{{·w}}[[Powerful number]]{{·w}}[[Perfect power]]{{·w}}[[Achilles number]]{{·w}}[[Smooth number]]{{·w}}[[Regular number]]{{·w}}[[Rough number]]{{·w}}[[Unusual number]]
+
* [[Prime number|Prime]]
{{nowrap end}}
+
* [[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
+
| group3 = Constrained divisor sums
|list3 = {{nowrap begin}}
+
| list3 =
[[Perfect number]]{{·w}}[[Almost perfect number]]{{·w}}[[Quasiperfect number]]{{·w}}[[Multiply perfect number]]{{·w}}[[Hyperperfect number]]{{·w}} [[Superperfect number]]{{·w}}[[Unitary perfect number]]{{·w}}[[Semiperfect number]]{{·w}}[[Primitive semiperfect number]]{{·w}}[[Practical number]]
+
* [[Perfect number|Perfect]]
{{nowrap end}}
+
* [[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 = With many divisors
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| group4 = With many divisors
|list4 = {{nowrap begin}}
+
| list4 =
[[Abundant number]]{{·w}}[[Primitive abundant number]]{{·w}}[[Highly abundant number]]{{·w}}[[Superabundant number]]{{·w}}[[Colossally abundant number]]{{·w}}[[Highly composite number]]{{·w}}[[Superior highly composite number]]{{·w}}[[Weird number]]
+
* [[Abundant number|Abundant]]
{{nowrap end}}
+
* [[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 = Related to [[aliquot sequence]]s
+
| group5 = [[Aliquot sequence]]-related
|list5 = {{nowrap begin}}
+
| list5 =
[[Untouchable number]]{{·w}}[[Amicable number]]{{·w}}[[Sociable number]]
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* [[Untouchable number|Untouchable]]
{{nowrap end}}
+
* [[Amicable numbers|Amicable]]
 +
* [[Sociable number|Sociable]]
 +
* [[Betrothed numbers|Betrothed]]
 +
 
 +
| group6 = [[Radix|Base]]-dependent
 +
| 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]]
  
|group6 = Other sets
 
|list6 = {{nowrap begin}}
 
[[Deficient number]]{{·w}}[[Friendly number]]{{·w}}[[Friendly number#Solitary numbers|Solitary number]]{{·w}}[[Sublime number]]{{·w}}[[Harmonic divisor number]]{{·w}}[[Frugal number]]{{·w}}[[Equidigital number]]{{·w}}[[Extravagant number]]
 
{{nowrap end}}
 
 
}}<noinclude>
 
}}<noinclude>
 +
{{documentation|content=
 +
 +
{{collapsible option |statename=optional |default=collapsed}}
  
[[Category:Mathematics templates|{{PAGENAME}}]]
+
==See also==
 +
*{{tl|Classes of natural numbers}}
  
[[eo:Ŝablono:Nombroj laŭ dividantoj]]
+
[[Category:Mathematics navigational boxes]]
[[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