Difference between revisions of "Template:Divisor classes"

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{| style="width: 15em; float: right; text-align: center; border: 2px solid #062; border-collapse: collapse; margin-left: 1em; margin-bottom: 1em; font-size: smaller;"
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{{Navbox
|-
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| name = Divisor classes
| style="text-align: center; padding: 0.5em; background: white; color: #062; font-size: medium;" | '''Divisibility-based<br/> sets of integers'''
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| state = {{{state|<includeonly>{{{1|collapsed}}}</includeonly>}}}
|-
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| title = Divisibility-based sets of integers
| style="padding-left: 1em; text-align: left; border-top: 1px solid #062;" | ''Forms of factorization:''
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| image = [[File:Lattice of the divisibility of 60.svg|175px|Divisibility of 60]]
|-
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| listclass = hlist
| [[Prime number]]
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|-
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| group1 = Overview
| [[Composite number]]
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| list1 =
|-
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* [[Integer factorization]]
| [[Powerful number]]
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* [[Divisor]]
|-
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* [[Unitary divisor]]
| [[Square-free integer|Square-free number]]
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* [[Divisor function]]
|-
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* [[Prime factor]]
| [[Achilles number]]
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* [[Fundamental theorem of arithmetic]]
|-
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| style="padding-left: 1em; text-align: left; border-top: 1px solid #062;" | ''Constrained divisor sums:''
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| group2 = Factorization forms
|-
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| list2 =
| [[Perfect number]]
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* [[Prime number|Prime]]
|-
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* [[Composite number|Composite]]
| [[Almost perfect number]]
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* [[Semiprime]]
|-
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* [[Pronic number|Pronic]]
| [[Quasiperfect number]]
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* [[Sphenic number|Sphenic]]
|-
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* [[Square-free integer|Square-free]]
| [[Multiply perfect number]]
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* [[Powerful number|Powerful]]
|-
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* [[Perfect power]]
| [[Hyperperfect number]]
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* [[Achilles number|Achilles]]
|-
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* [[Smooth number|Smooth]]
| [[Superperfect number]]
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* [[Regular number|Regular]]
|-
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* [[Rough number|Rough]]
| [[Unitary perfect number]]
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* [[Unusual number|Unusual]]
|-
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| [[Semiperfect number]]
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| group3 = Constrained divisor sums
|-
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| list3 =
| [[Primitive semiperfect number]]
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* [[Perfect number|Perfect]]
|-
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* [[Almost perfect number|Almost perfect]]
| [[Practical number]]
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* [[Quasiperfect number|Quasiperfect]]
|-
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* [[Multiply perfect number|Multiply perfect]]
| style="padding-left: 1em; text-align: left; border-top: 1px solid #062;" | ''Numbers with many divisors:''
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* [[Hemiperfect number|Hemiperfect]]
|-
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* [[Hyperperfect number|Hyperperfect]]
| [[Abundant number]]
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* [[Superperfect number|Superperfect]]
|-
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* [[Unitary perfect number|Unitary perfect]]
| [[Primitive abundant number]]
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* [[Semiperfect number|Semiperfect]]
|-
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* [[Practical number|Practical]]
| [[Highly abundant number]]
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* [[Erdős–Nicolas number|Erdős–Nicolas]]
|-
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| [[Superabundant number]]
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| group4 = With many divisors
|-
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| list4 =
| [[Colossally abundant number]]
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* [[Abundant number|Abundant]]
|-
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* [[Primitive abundant number|Primitive abundant]]
| [[Highly composite number]]
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* [[Highly abundant number|Highly abundant]]
|-
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* [[Superabundant number|Superabundant]]
| [[Superior highly composite number]]
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* [[Colossally abundant number|Colossally abundant]]
|-
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* [[Highly composite number|Highly composite]]
| style="padding-left: 1em; text-align: left; border-top: 1px solid #062;" | ''Other:''
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* [[Superior highly composite number|Superior highly composite]]
|-
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* [[Weird number|Weird]]
| [[Untouchable number]]
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|-
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| group5 = [[Aliquot sequence]]-related
| [[Deficient number]]
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| list5 =
|-
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* [[Untouchable number|Untouchable]]
| [[Weird number]]
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* [[Amicable numbers|Amicable]]
|-
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* [[Sociable number|Sociable]]
| [[Amicable number]]
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* [[Betrothed numbers|Betrothed]]
|-
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| [[Friendly number]]
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| group6 = [[Radix|Base]]-dependent
|-
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| list6 =
| [[Sociable number]]
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* [[Equidigital number|Equidigital]]
|-
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* [[Extravagant number|Extravagant]]
| [[Solitary number]]
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* [[Frugal number|Frugal]]
|-
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* [[Harshad number|Harshad]]
| [[Sublime number]]
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* [[Polydivisible number|Polydivisible]]
|-
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* [[Smith number|Smith]]
| [[Harmonic divisor number]]
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|-
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| group7 = Other sets
| [[Frugal number]]
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| list7 =
|-
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* [[Arithmetic number|Arithmetic]]
| [[Equidigital number]]
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* [[Deficient number|Deficient]]
|-
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* [[Friendly number|Friendly]]
| [[Extravagant number]]
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* [[Friendly number#Solitary numbers|Solitary]]
|-
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* [[Sublime number|Sublime]]
| style="padding-left: 1em; text-align: left; border-top: 1px solid #062;" | ''See also:''
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* [[Harmonic divisor number|Harmonic divisor]]
|-
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* [[Descartes number|Descartes]]
| [[Divisor function]]
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* [[Refactorable number|Refactorable]]
|-
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* [[Superperfect number|Superperfect]]
| [[Divisor]]
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|-
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}}<noinclude>
| [[Prime factor]]
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{{documentation|content=
|-
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| [[Factorization]]
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{{collapsible option |statename=optional |default=collapsed}}
|-
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| style="text-align: right;" | {{navbar|Divisor classes}}
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==See also==
|}
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*{{tl|Classes of natural numbers}}
<noinclude>
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[[Category:Mathematics templates|{{PAGENAME}}]]
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[[Category:Mathematics navigational boxes]]
[[eo:Ŝablono:Nombroj laŭ dividantoj]]
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}}
[[fr:Modèle: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