Difference between revisions of "Template:Divisor classes"
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imported>Marqaz (added Erdős–Nicolas number) |
imported>PrimeHunter (Undid revision 954673663 by 87.95.193.244 (talk). No good reason for a red link here) |
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| state = {{{state|<includeonly>{{{1|collapsed}}}</includeonly>}}} | | 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| | + | | image = [[File:Lattice of the divisibility of 60.svg|175px|Divisibility of 60]] |
| listclass = hlist | | listclass = hlist | ||
| Line 14: | Line 14: | ||
* [[Prime factor]] | * [[Prime factor]] | ||
* [[Fundamental theorem of arithmetic]] | * [[Fundamental theorem of arithmetic]] | ||
| − | |||
| group2 = Factorization forms | | group2 = Factorization forms | ||
| list2 = | | list2 = | ||
| − | * [[Prime number]] | + | * [[Prime number|Prime]] |
| − | * [[Composite number]] | + | * [[Composite number|Composite]] |
| − | * [[Semiprime | + | * [[Semiprime]] |
| − | * [[Pronic number]] | + | * [[Pronic number|Pronic]] |
| − | * [[Sphenic number]] | + | * [[Sphenic number|Sphenic]] |
| − | * [[Square-free integer|Square-free | + | * [[Square-free integer|Square-free]] |
| − | * [[Powerful number]] | + | * [[Powerful number|Powerful]] |
* [[Perfect power]] | * [[Perfect power]] | ||
| − | * [[Achilles number]] | + | * [[Achilles number|Achilles]] |
| − | * [[Smooth number]] | + | * [[Smooth number|Smooth]] |
| − | * [[Regular number]] | + | * [[Regular number|Regular]] |
| − | * [[Rough number]] | + | * [[Rough number|Rough]] |
| − | * [[Unusual number]] | + | * [[Unusual number|Unusual]] |
| group3 = Constrained divisor sums | | group3 = Constrained divisor sums | ||
| list3 = | | list3 = | ||
| − | * [[Perfect number]] | + | * [[Perfect number|Perfect]] |
| − | * [[Almost perfect number]] | + | * [[Almost perfect number|Almost perfect]] |
| − | * [[Quasiperfect number]] | + | * [[Quasiperfect number|Quasiperfect]] |
| − | * [[Multiply perfect number]] | + | * [[Multiply perfect number|Multiply perfect]] |
| − | * [[Hemiperfect number]] | + | * [[Hemiperfect number|Hemiperfect]] |
| − | * [[Hyperperfect number]] | + | * [[Hyperperfect number|Hyperperfect]] |
| − | * [[Superperfect number]] | + | * [[Superperfect number|Superperfect]] |
| − | * [[Unitary perfect number]] | + | * [[Unitary perfect number|Unitary perfect]] |
| − | * [[Semiperfect number]] | + | * [[Semiperfect number|Semiperfect]] |
| − | * [[Practical number]] | + | * [[Practical number|Practical]] |
| − | * [[Erdős–Nicolas number]] | + | * [[Erdős–Nicolas number|Erdős–Nicolas]] |
| − | |||
| group4 = With many divisors | | group4 = With many divisors | ||
| list4 = | | list4 = | ||
| − | * [[Abundant number]] | + | * [[Abundant number|Abundant]] |
| − | * [[Primitive abundant number]] | + | * [[Primitive abundant number|Primitive abundant]] |
| − | * [[Highly abundant number]] | + | * [[Highly abundant number|Highly abundant]] |
| − | * [[Superabundant number]] | + | * [[Superabundant number|Superabundant]] |
| − | * [[Colossally abundant number]] | + | * [[Colossally abundant number|Colossally abundant]] |
| − | * [[Highly composite number]] | + | * [[Highly composite number|Highly composite]] |
| − | * [[Superior highly composite number]] | + | * [[Superior highly composite number|Superior highly composite]] |
| − | * [[Weird number]] | + | * [[Weird number|Weird]] |
| group5 = [[Aliquot sequence]]-related | | group5 = [[Aliquot sequence]]-related | ||
| list5 = | | list5 = | ||
| − | * [[Untouchable number]] | + | * [[Untouchable number|Untouchable]] |
| − | * [[Amicable numbers|Amicable | + | * [[Amicable numbers|Amicable]] |
| − | * [[Sociable number]] | + | * [[Sociable number|Sociable]] |
| − | * [[Betrothed numbers|Betrothed | + | * [[Betrothed numbers|Betrothed]] |
| − | | group6 = | + | | group6 = [[Radix|Base]]-dependent |
| list6 = | | list6 = | ||
| − | * [[Deficient number]] | + | * [[Equidigital number|Equidigital]] |
| − | * [[Friendly number]] | + | * [[Extravagant number|Extravagant]] |
| − | * [[Friendly number#Solitary numbers|Solitary | + | * [[Frugal number|Frugal]] |
| − | * [[Sublime number]] | + | * [[Harshad number|Harshad]] |
| − | * [[Harmonic divisor number]] | + | * [[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> | }}<noinclude> | ||
| + | {{documentation|content= | ||
| + | {{collapsible option |statename=optional |default=collapsed}} | ||
| − | {{ | + | ==See also== |
| + | *{{tl|Classes of natural numbers}} | ||
[[Category:Mathematics navigational boxes]] | [[Category:Mathematics navigational boxes]] | ||
| − | + | }} | |
</noinclude> | </noinclude> | ||
Latest revision as of 08:39, 19 December 2020
50px 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}}
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
| Editors can experiment in this template's sandbox (create | mirror) and testcases (create) pages. Subpages of this template. |