Difference between revisions of "Template:Classes of natural numbers"

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imported>David Eppstein
Line 52: Line 52:
 
|group5 = Possessing a<br/> specific set<br/> of other numbers
 
|group5 = Possessing a<br/> specific set<br/> of other numbers
 
|list5 =  
 
|list5 =  
* [[Congruent number|Congruent]]
 
 
* [[Knödel number|Knödel]]
 
* [[Knödel number|Knödel]]
 
* [[Riesel number|Riesel]]
 
* [[Riesel number|Riesel]]
Line 83: Line 82:
 
* [[Centered square number|Centered square]]
 
* [[Centered square number|Centered square]]
 
* [[Centered pentagonal number|Centered pentagonal]]
 
* [[Centered pentagonal number|Centered pentagonal]]
* [[Centered hexagonal number|Centered hexagonal (hex)]]
+
* [[Centered hexagonal number|Centered hexagonal]]
 
* [[Centered heptagonal number|Centered heptagonal]]
 
* [[Centered heptagonal number|Centered heptagonal]]
 
* [[Centered octagonal number|Centered octagonal]]
 
* [[Centered octagonal number|Centered octagonal]]
 
* [[Centered nonagonal number|Centered nonagonal]]
 
* [[Centered nonagonal number|Centered nonagonal]]
 
* [[Centered decagonal number|Centered decagonal]]
 
* [[Centered decagonal number|Centered decagonal]]
* [[Centered hendecagonal number|Centered hendecagonal]]
+
* [[Star number|Star]]
* [[Star number|Centered dodecagonal (star)]]
 
  
 
   | group2 = [[Polygonal number|non-centered]]
 
   | group2 = [[Polygonal number|non-centered]]
Line 95: Line 93:
 
* [[Triangular number|Triangular]]
 
* [[Triangular number|Triangular]]
 
* [[Square number|Square]]
 
* [[Square number|Square]]
* [[Pronic number|Pronic]]
 
 
* [[Square triangular number|Square triangular]]
 
* [[Square triangular number|Square triangular]]
 
* [[Pentagonal number|Pentagonal]]
 
* [[Pentagonal number|Pentagonal]]
Line 103: Line 100:
 
* [[Nonagonal number|Nonagonal]]
 
* [[Nonagonal number|Nonagonal]]
 
* [[Decagonal number|Decagonal]]
 
* [[Decagonal number|Decagonal]]
* [[Hendecagonal number|Hendecagonal]]
 
 
* [[Dodecagonal number|Dodecagonal]]
 
* [[Dodecagonal number|Dodecagonal]]
 
}}
 
}}
Line 120: Line 116:
 
   | list2 =  
 
   | list2 =  
 
* [[Tetrahedral number|Tetrahedral]]
 
* [[Tetrahedral number|Tetrahedral]]
* [[Cube number|Cube]]
 
 
* [[Octahedral number|Octahedral]]
 
* [[Octahedral number|Octahedral]]
 
* [[Dodecahedral number|Dodecahedral]]
 
* [[Dodecahedral number|Dodecahedral]]
Line 128: Line 123:
 
   | group3 = [[Pyramidal number|pyramidal]]
 
   | group3 = [[Pyramidal number|pyramidal]]
 
   | list3 =  
 
   | list3 =  
* [[Tetrahedral number|Triangle pyramidal]]
 
 
* [[Square pyramidal number|Square pyramidal]]
 
* [[Square pyramidal number|Square pyramidal]]
 
* [[Pentagonal pyramidal number|Pentagonal pyramidal]]
 
* [[Pentagonal pyramidal number|Pentagonal pyramidal]]
Line 158: Line 152:
 
* [[Frobenius pseudoprime]]
 
* [[Frobenius pseudoprime]]
 
* [[Lucas pseudoprime]]
 
* [[Lucas pseudoprime]]
* [[Lucas–Carmichael number]]
 
 
* [[Somer–Lucas pseudoprime]]
 
* [[Somer–Lucas pseudoprime]]
 
* [[Strong pseudoprime]]
 
* [[Strong pseudoprime]]
Line 183: Line 176:
 
  |group1 = By properties of [[Divisor function|σ(''n'')]]
 
  |group1 = By properties of [[Divisor function|σ(''n'')]]
 
  |list1 =  
 
  |list1 =  
 +
* [[Abundant number|Abundant]]
 
* [[Almost perfect number|Almost perfect]]
 
* [[Almost perfect number|Almost perfect]]
 
* [[Arithmetic number|Arithmetic]]
 
* [[Arithmetic number|Arithmetic]]
Line 201: Line 195:
 
* [[Superior highly composite number|Superior highly composite]]
 
* [[Superior highly composite number|Superior highly composite]]
 
* [[Superperfect number|Superperfect]]
 
* [[Superperfect number|Superperfect]]
 +
* [[Untouchable number|Untouchable]]
  
 
  |group2 = By properties of [[Arithmetic function#Ω(n), ω(n), νp(n) – prime power decomposition|Ω(''n'')]]
 
  |group2 = By properties of [[Arithmetic function#Ω(n), ω(n), νp(n) – prime power decomposition|Ω(''n'')]]
 
  |list2 =
 
  |list2 =
 
* [[Almost prime]]
 
* [[Almost prime]]
* [[Composite number|Composite]]
 
* [[Prime number|Prime]]
 
 
* [[Semiprime]]
 
* [[Semiprime]]
  
Line 220: Line 213:
 
  |group4 = By properties of [[Divisor function#Definition|s(''n'')]]
 
  |group4 = By properties of [[Divisor function#Definition|s(''n'')]]
 
  |list4 =  
 
  |list4 =  
* [[Abundant number|Abundant]]
 
 
* [[Amicable numbers|Amicable]]
 
* [[Amicable numbers|Amicable]]
 
* [[Betrothed numbers|Betrothed]]
 
* [[Betrothed numbers|Betrothed]]
 
* [[Deficient number|Deficient]]
 
* [[Deficient number|Deficient]]
 
* [[Semiperfect number|Semiperfect]]
 
* [[Semiperfect number|Semiperfect]]
* [[Sociable number|Sociable]]
 
* [[Untouchable number|Untouchable]]
 
* [[Weird number|Weird]]
 
 
}}
 
}}
 
* [[Euclid number|Euclid]]
 
* [[Euclid number|Euclid]]
Line 245: Line 234:
 
* [[Erdős–Woods number|Erdős–Woods]]
 
* [[Erdős–Woods number|Erdős–Woods]]
 
* [[Friendly number|Friendly]]
 
* [[Friendly number|Friendly]]
 +
* [[Frugal number|Frugal]]
 
* [[Giuga number|Giuga]]
 
* [[Giuga number|Giuga]]
 
* [[Harmonic divisor number|Harmonic divisor]]
 
* [[Harmonic divisor number|Harmonic divisor]]
 +
* [[Lucas–Carmichael number|Lucas–Carmichael]]
 +
* [[Pronic number|Pronic]]
 
* [[Regular number|Regular]]
 
* [[Regular number|Regular]]
 
* [[Rough number|Rough]]
 
* [[Rough number|Rough]]
 
* [[Smooth number|Smooth]]
 
* [[Smooth number|Smooth]]
 +
* [[Sociable number|Sociable]]
 
* [[Sphenic number|Sphenic]]
 
* [[Sphenic number|Sphenic]]
 
* [[Størmer number|Størmer]]
 
* [[Størmer number|Størmer]]
Line 267: Line 260:
 
* [[Factorion]]
 
* [[Factorion]]
 
* [[Friedman number|Friedman]]
 
* [[Friedman number|Friedman]]
* [[Frugal number|Frugal]]
 
 
* [[Happy number|Happy]]
 
* [[Happy number|Happy]]
 
* [[Harshad number|Harshad]]
 
* [[Harshad number|Harshad]]
Line 286: Line 278:
 
* [[Self-descriptive number|Self-descriptive]]
 
* [[Self-descriptive number|Self-descriptive]]
 
* [[Smarandache–Wellin number|Smarandache–Wellin]]
 
* [[Smarandache–Wellin number|Smarandache–Wellin]]
* [[Smith number|Smith]]
 
 
* [[Strictly non-palindromic number|Strictly non-palindromic]]
 
* [[Strictly non-palindromic number|Strictly non-palindromic]]
 
* [[Strobogrammatic number|Strobogrammatic]]
 
* [[Strobogrammatic number|Strobogrammatic]]

Revision as of 16:28, 21 April 2019

Template documentation

Initial visibility: currently defaults to autocollapse

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

  • |state=collapsed: {{Classes of natural numbers|state=collapsed}} to show the template collapsed, i.e., hidden apart from its title bar
  • |state=expanded: {{Classes of natural numbers|state=expanded}} to show the template expanded, i.e., fully visible
  • |state=autocollapse: {{Classes of natural numbers|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 autocollapse.

See also