Difference between revisions of "Template:Classes of natural numbers"
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(Mention squares (can't believe they were not here) and perfect powers) |
imported>Vpab15 m (update to Sierpiński number) |
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− | {{Navbox | + | {{Navbox with collapsible groups |
| name = Classes of natural numbers | | name = Classes of natural numbers | ||
| title = Classes of [[natural number]]s | | title = Classes of [[natural number]]s | ||
| listclass = hlist | | listclass = hlist | ||
− | | state = {{{state|collapsed}}} | + | | state = {{{state|<includeonly>collapsed</includeonly>}}} |
− | |group1 = [[Exponentiation|Powers]] and | + | |group1 = [[Exponentiation|Powers]] and related numbers |
|list1 = | |list1 = | ||
− | * [[Achilles number]] | + | * [[Achilles number|Achilles]] |
− | * [[Power of two| | + | * [[Power of two|Power of 2]] |
− | * [[Square number|Square]] | + | * [[Power of three|Power of 3]] |
− | * [[Cube (algebra)| | + | * [[Power of 10]] |
− | * [[Fourth power]] | + | * [[Square number|Square]] |
− | * [[Fifth power (algebra)|Fifth | + | * [[Cube (algebra)|Cube]] |
− | * [[Perfect power]] | + | * [[Fourth power]] |
− | * [[Powerful number]] | + | * [[Fifth power (algebra)|Fifth power]] |
+ | * [[Sixth power]] | ||
+ | * [[Seventh power]] | ||
+ | * [[Eighth power]] | ||
+ | * [[Perfect power]] | ||
+ | * [[Powerful number|Powerful]] | ||
+ | * [[Prime power]] | ||
− | |group2 = Of the form | + | |group2 = Of the form ''a'' × 2<sup>''b''</sup> ± 1 |
|list2 = | |list2 = | ||
− | * [[Cullen number]] | + | * [[Cullen number|Cullen]] |
− | * [[Double Mersenne number]] | + | * [[Double Mersenne number|Double Mersenne]] |
− | * [[Fermat number]] | + | * [[Fermat number|Fermat]] |
− | * [[Mersenne | + | * [[Mersenne prime|Mersenne]] |
− | * [[Proth number]] | + | * [[Proth number|Proth]] |
− | * [[Thabit number]] | + | * [[Thabit number|Thabit]] |
− | * [[Woodall number]] | + | * [[Woodall number|Woodall]] |
− | |group3 = | + | |group3 = Other polynomial numbers |
|list3 = | |list3 = | ||
− | * [[Carol number]] | + | * [[Carol number|Carol]] |
− | * [[Hilbert number]] | + | * [[Hilbert number|Hilbert]] |
− | * [[Idoneal number]] | + | * [[Idoneal number|Idoneal]] |
− | * [[Kynea number]] | + | * [[Kynea number|Kynea]] |
− | * [[Leyland number]] | + | * [[Leyland number|Leyland]] |
+ | * [[Loeschian number|Loeschian]] | ||
* [[Lucky numbers of Euler]] | * [[Lucky numbers of Euler]] | ||
− | |group4 = [[Recursion|Recursively]] defined | + | |group4 = [[Recursion|Recursively]] defined numbers |
|list4 = | |list4 = | ||
− | * [[Fibonacci number]] | + | * [[Fibonacci number|Fibonacci]] |
− | * [[Jacobsthal number]] | + | * [[Jacobsthal number|Jacobsthal]] |
− | * [[Leonardo number]] | + | * [[Leonardo number|Leonardo]] |
− | * [[Pell number]] | + | * [[Lucas number|Lucas]] |
− | * [[Perrin number]] | + | * [[Padovan sequence|Padovan]] |
− | + | * [[Pell number|Pell]] | |
− | |group5 = Possessing a | + | * [[Perrin number|Perrin]] |
+ | |group5 = Possessing a specific set of other numbers | ||
|list5 = | |list5 = | ||
− | * [[Knödel number]] | + | * [[Knödel number|Knödel]] |
− | * [[Riesel number]] | + | * [[Riesel number|Riesel]] |
− | * [[ | + | * [[Sierpiński number|Sierpiński]] |
− | |group6 = Expressible via | + | |group6 = Expressible via specific sums |
|list6 = | |list6 = | ||
− | * [[Nonhypotenuse number]] | + | * [[Nonhypotenuse number|Nonhypotenuse]] |
− | * [[Polite number]] | + | * [[Polite number|Polite]] |
− | * [[Practical number]] | + | * [[Practical number|Practical]] |
− | * [[Primary pseudoperfect number]] | + | * [[Primary pseudoperfect number|Primary pseudoperfect]] |
− | * [[Ulam number]] | + | * [[Ulam number|Ulam]] |
− | * [[Wolstenholme number | + | * [[Wolstenholme number|Wolstenholme]] |
− | |||
− | | | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | | | + | |group7 = [[Figurate number]]s |
− | | | + | |list7 = {{Navbox|subgroup |
| group1 = [[Two-dimensional space|2-dimensional]] | | group1 = [[Two-dimensional space|2-dimensional]] | ||
− | | list1 = {{Navbox subgroup | + | | list1 = {{Navbox|subgroup |
| group1 = [[Centered polygonal number|centered]] | | group1 = [[Centered polygonal number|centered]] | ||
| list1 = | | list1 = | ||
− | * [[Centered triangular number]] | + | * [[Centered triangular number|Centered triangular]] |
− | * [[Centered square number]] | + | * [[Centered square number|Centered square]] |
− | * [[Centered pentagonal number]] | + | * [[Centered pentagonal number|Centered pentagonal]] |
− | * [[Centered hexagonal number]] | + | * [[Centered hexagonal number|Centered hexagonal]] |
− | * [[Centered heptagonal number]] | + | * [[Centered heptagonal number|Centered heptagonal]] |
− | * [[Centered octagonal number]] | + | * [[Centered octagonal number|Centered octagonal]] |
− | * [[Centered nonagonal number]] | + | * [[Centered nonagonal number|Centered nonagonal]] |
− | * [[Centered decagonal number]] | + | * [[Centered decagonal number|Centered decagonal]] |
− | * [[Star number]] | + | * [[Star number|Star]] |
| group2 = [[Polygonal number|non-centered]] | | group2 = [[Polygonal number|non-centered]] | ||
| list2 = | | list2 = | ||
− | * [[Triangular number]] | + | * [[Triangular number|Triangular]] |
− | * [[Pentagonal number]] | + | * [[Square number|Square]] |
− | * [[Hexagonal number]] | + | * [[Square triangular number|Square triangular]] |
− | * [[Heptagonal number]] | + | * [[Pentagonal number|Pentagonal]] |
− | * [[Octagonal number]] | + | * [[Hexagonal number|Hexagonal]] |
− | * [[Nonagonal number]] | + | * [[Heptagonal number|Heptagonal]] |
− | * [[Decagonal number]] | + | * [[Octagonal number|Octagonal]] |
− | * [[Dodecagonal number]] | + | * [[Nonagonal number|Nonagonal]] |
+ | * [[Decagonal number|Decagonal]] | ||
+ | * [[Dodecagonal number|Dodecagonal]] | ||
}} | }} | ||
| group2 = [[Three-dimensional space|3-dimensional]] | | group2 = [[Three-dimensional space|3-dimensional]] | ||
− | | list2 = {{Navbox subgroup | + | | list2 = {{Navbox|subgroup |
| group1 = [[centered polyhedral number|centered]] | | group1 = [[centered polyhedral number|centered]] | ||
| list1 = | | list1 = | ||
− | * [[Centered tetrahedral number]] | + | * [[Centered tetrahedral number|Centered tetrahedral]] |
− | * [[Centered cube number]] | + | * [[Centered cube number|Centered cube]] |
− | * [[Centered octahedral number]] | + | * [[Centered octahedral number|Centered octahedral]] |
− | * [[Centered dodecahedral number]] | + | * [[Centered dodecahedral number|Centered dodecahedral]] |
− | * [[Centered icosahedral number]] | + | * [[Centered icosahedral number|Centered icosahedral]] |
| group2 = [[Polyhedral number|non-centered]] | | group2 = [[Polyhedral number|non-centered]] | ||
| list2 = | | list2 = | ||
− | * [[Tetrahedral number]] | + | * [[Tetrahedral number|Tetrahedral]] |
− | * [[Octahedral number]] | + | * [[Cube (algebra)|Cubic]] |
− | * [[Dodecahedral number]] | + | * [[Octahedral number|Octahedral]] |
− | * [[Icosahedral number]] | + | * [[Dodecahedral number|Dodecahedral]] |
− | * [[Stella octangula number]] | + | * [[Icosahedral number|Icosahedral]] |
+ | * [[Stella octangula number|Stella octangula]] | ||
| group3 = [[Pyramidal number|pyramidal]] | | group3 = [[Pyramidal number|pyramidal]] | ||
| list3 = | | list3 = | ||
− | * [[Square pyramidal number]] | + | * [[Square pyramidal number|Square pyramidal]] |
− | * [[Pentagonal pyramidal number]] | + | * [[Pentagonal pyramidal number|Pentagonal pyramidal]] |
− | * [[Hexagonal pyramidal number]] | + | * [[Hexagonal pyramidal number|Hexagonal pyramidal]] |
− | * [[Heptagonal pyramidal number]] | + | * [[Heptagonal pyramidal number|Heptagonal pyramidal]] |
}} | }} | ||
| group3 = [[Four-dimensional space|4-dimensional]] | | group3 = [[Four-dimensional space|4-dimensional]] | ||
− | | list3 = {{Navbox subgroup | + | | list3 = {{Navbox|subgroup |
|group1 = centered | |group1 = centered | ||
|list1 = | |list1 = | ||
− | |||
− | |||
− | |||
|group2 = non-centered | |group2 = non-centered | ||
|list2 = | |list2 = | ||
− | * [[Pentatope number]] | + | * [[Pentatope number|Pentatope]] |
+ | * [[Squared triangular number|Squared triangular]] | ||
+ | * [[Fourth power|Tesseractic]] | ||
}} | }} | ||
}} | }} | ||
+ | |||
+ | |group8 = Combinatorial numbers | ||
+ | |list8 = | ||
+ | * [[Bell number|Bell]] | ||
+ | * [[Cake number|Cake]] | ||
+ | * [[Catalan number|Catalan]] | ||
+ | * [[Dedekind number|Dedekind]] | ||
+ | * [[Delannoy number|Delannoy]] | ||
+ | * [[Euler number|Euler]] | ||
+ | * [[Fuss–Catalan number|Fuss–Catalan]] | ||
+ | * [[Lazy caterer's sequence]] | ||
+ | * [[Lobb number|Lobb]] | ||
+ | * [[Motzkin number|Motzkin]] | ||
+ | * [[Narayana number|Narayana]] | ||
+ | * [[Ordered Bell number|Ordered Bell]] | ||
+ | * [[Schröder number|Schröder]] | ||
+ | * [[Schröder–Hipparchus number|Schröder–Hipparchus]] | ||
+ | |||
+ | |group9 = [[Prime number|Primes]] | ||
+ | |list9 = | ||
+ | * [[Wieferich prime#Wieferich numbers|Wieferich]] | ||
+ | * [[Wall–Sun–Sun prime|Wall–Sun–Sun]] | ||
+ | * [[Wolstenholme prime]] | ||
+ | * [[Wilson prime#Wilson numbers|Wilson]] | ||
|group10 = [[Pseudoprime]]s | |group10 = [[Pseudoprime]]s | ||
|list10 = | |list10 = | ||
− | * [[Carmichael number]] | + | * [[Carmichael number]] |
− | * [[Catalan pseudoprime]] | + | * [[Catalan pseudoprime]] |
− | * [[Elliptic pseudoprime]] | + | * [[Elliptic pseudoprime]] |
− | * [[Euler pseudoprime]] | + | * [[Euler pseudoprime]] |
− | * [[Euler–Jacobi pseudoprime]] | + | * [[Euler–Jacobi pseudoprime]] |
− | * [[Fermat pseudoprime]] | + | * [[Fermat pseudoprime]] |
− | * [[ | + | * [[Frobenius pseudoprime]] |
− | * [[ | + | * [[Lucas pseudoprime]] |
− | * [[ | + | * [[Lucas–Carmichael number]] |
− | * [[Somer–Lucas pseudoprime]] | + | * [[Somer–Lucas pseudoprime]] |
− | * [[Strong pseudoprime]]s | + | * [[Strong pseudoprime]] |
+ | |||
+ | |group11 = [[Arithmetic function]]s and [[Arithmetic dynamics|dynamics]] | ||
+ | |list11 = {{Navbox|subgroup | ||
+ | |group1 = [[Divisor function]]s | ||
+ | |list1 = | ||
+ | * [[Abundant number|Abundant]] | ||
+ | * [[Almost perfect number|Almost perfect]] | ||
+ | * [[Arithmetic number|Arithmetic]] | ||
+ | * [[Betrothed numbers|Betrothed]] | ||
+ | * [[Colossally abundant number|Colossally abundant]] | ||
+ | * [[Deficient number|Deficient]] | ||
+ | * [[Descartes number|Descartes]] | ||
+ | * [[Hemiperfect number|Hemiperfect]] | ||
+ | * [[Highly abundant number|Highly abundant]] | ||
+ | * [[Highly composite number|Highly composite]] | ||
+ | * [[Hyperperfect number|Hyperperfect]] | ||
+ | * [[Multiply perfect number|Multiply perfect]] | ||
+ | * [[Perfect number|Perfect]] | ||
+ | * [[Practical number|Practical]] | ||
+ | * [[Primitive abundant number|Primitive abundant]] | ||
+ | * [[Quasiperfect number|Quasiperfect]] | ||
+ | * [[Refactorable number|Refactorable]] | ||
+ | * [[Semiperfect number|Semiperfect]] | ||
+ | * [[Sublime number|Sublime]] | ||
+ | * [[Superabundant number|Superabundant]] | ||
+ | * [[Superior highly composite number|Superior highly composite]] | ||
+ | * [[Superperfect number|Superperfect]] | ||
− | | | + | |group3 = [[Euler's totient function]] |
− | + | |list3 = | |
− | + | * [[Highly cototient number|Highly cototient]] | |
− | + | * [[Highly totient number|Highly totient]] | |
− | + | * [[Noncototient]] | |
− | * [[ | + | * [[Nontotient]] |
− | + | * [[Perfect totient number|Perfect totient]] | |
− | * [[ | + | * [[Sparsely totient number|Sparsely totient]] |
− | * [[ | ||
− | * [[ | ||
− | * [[ | ||
− | * [[ | ||
− | | | + | |group2 = [[Prime omega function]]s |
− | |list12 = {{Navbox subgroup | + | |list2 = |
− | |group1 = | + | * [[Almost prime]] |
+ | * [[Semiprime]] | ||
+ | |||
+ | |group5 = [[Aliquot sequence]]s | ||
+ | |list5 = | ||
+ | * [[Amicable numbers|Amicable]] | ||
+ | * [[Perfect number|Perfect]] | ||
+ | * [[Sociable numbers|Sociable]] | ||
+ | * [[Untouchable number|Untouchable]] | ||
+ | |||
+ | |group6 = [[Primorial]] | ||
+ | |list6 = | ||
+ | * [[Euclid number|Euclid]] | ||
+ | * [[Fortunate number|Fortunate]] | ||
+ | }} | ||
+ | |||
+ | |group12 = Other [[prime factor]] or [[divisor]] related numbers | ||
+ | |list12 = | ||
+ | * [[Blum integer|Blum]] | ||
+ | * [[Erdős–Nicolas number|Erdős–Nicolas]] | ||
+ | * [[Erdős–Woods number|Erdős–Woods]] | ||
+ | * [[Friendly number|Friendly]] | ||
+ | * [[Giuga number|Giuga]] | ||
+ | * [[Harmonic divisor number|Harmonic divisor]] | ||
+ | * [[Lucas–Carmichael number|Lucas–Carmichael]] | ||
+ | * [[Pronic number|Pronic]] | ||
+ | * [[Regular number|Regular]] | ||
+ | * [[Rough number|Rough]] | ||
+ | * [[Smooth number|Smooth]] | ||
+ | * [[Sphenic number|Sphenic]] | ||
+ | * [[Størmer number|Størmer]] | ||
+ | * [[Super-Poulet number|Super-Poulet]] | ||
+ | * [[Zeisel number|Zeisel]] | ||
+ | |||
+ | |group13 = [[Numeral system]]-dependent numbers | ||
+ | |list13 = {{Navbox|subgroup | ||
+ | |group1 = [[Arithmetic function]]s and [[Arithmetic dynamics|dynamics]] | ||
|list1 = | |list1 = | ||
− | * [[ | + | * [[Persistence of a number|Persistence]] |
− | * | + | ** [[Additive persistence|Additive]] |
− | * [[ | + | ** [[Multiplicative persistence|Multiplicative]] |
− | * | + | {{Navbox|subgroup |
− | * [[ | + | |group1 = [[Digit sum]] |
− | + | |list1 = | |
− | + | * [[Digit sum]] | |
− | + | * [[Digital root]] | |
− | * [[ | + | * [[Self number|Self]] |
− | * [[ | + | * [[Sum-product number|Sum-product]] |
− | |||
− | |||
− | |||
− | |||
− | |||
− | * [[ | ||
− | * [[ | ||
− | + | |group2 = Digit product | |
+ | |list2 = | ||
+ | * [[Multiplicative digital root]] | ||
+ | * [[Sum-product number|Sum-product]] | ||
+ | |||
+ | |group3 = Coding-related | ||
+ | |list3 = | ||
+ | * [[Meertens number|Meertens]] | ||
+ | |||
+ | |group4 = Other | ||
+ | |list4 = | ||
+ | * [[Dudeney number|Dudeney]] | ||
+ | * [[Factorion]] | ||
+ | * [[Kaprekar number|Kaprekar]] | ||
+ | * [[Kaprekar's routine|Kaprekar's constant]] | ||
+ | * [[Keith number|Keith]] | ||
+ | * [[Lychrel number|Lychrel]] | ||
+ | * [[Narcissistic number|Narcissistic]] | ||
+ | * [[Perfect digit-to-digit invariant]] | ||
+ | * [[Perfect digital invariant]] | ||
+ | ** [[Happy number|Happy]] | ||
+ | }} | ||
+ | |group2 = [[P-adic numbers]]-related | ||
|list2 = | |list2 = | ||
− | * [[ | + | * [[Automorphic number|Automorphic]] |
− | * [[ | + | ** [[Trimorphic number|Trimorphic]] |
− | |group3 = | + | |group3 = [[Numerical digit|Digit]]-composition related |
|list3 = | |list3 = | ||
− | * [[ | + | * [[Palindromic number|Palindromic]] |
− | * [[ | + | * [[Pandigital number|Pandigital]] |
− | * [[ | + | * [[Repdigit]] |
− | * [[ | + | * [[Repunit]] |
− | * [[ | + | * [[Self-descriptive number|Self-descriptive]] |
− | * [[ | + | * [[Smarandache–Wellin number|Smarandache–Wellin]] |
+ | * [[Strictly non-palindromic number|Strictly non-palindromic]] | ||
+ | * [[Undulating number|Undulating]] | ||
− | |group4 = | + | |group4 = Digit-[[permutation]] related |
|list4 = | |list4 = | ||
− | * [[ | + | * [[Cyclic number|Cyclic]] |
− | * [[ | + | * [[Digit-reassembly number|Digit-reassembly]] |
− | * [[ | + | * [[Parasitic number|Parasitic]] |
− | * [[ | + | * [[Primeval number|Primeval]] |
+ | * [[Transposable integer|Transposable]] | ||
+ | |||
+ | |group5 = Divisor-related | ||
+ | |list5 = | ||
+ | * [[Equidigital number|Equidigital]] | ||
+ | * [[Extravagant number|Extravagant]] | ||
+ | * [[Frugal number|Frugal]] | ||
+ | * [[Harshad number|Harshad]] | ||
+ | * [[Polydivisible number|Polydivisible]] | ||
+ | * [[Smith number|Smith]] | ||
+ | * [[Vampire number|Vampire]] | ||
+ | |||
+ | |group6 = Other | ||
+ | |list6 = | ||
+ | * [[Friedman number|Friedman]] | ||
}} | }} | ||
− | |||
− | |||
− | | | + | |group14 = [[Binary number]]s |
− | | | + | |list14 = |
− | * [[ | + | * [[Evil number|Evil]] |
− | * [[ | + | * [[Odious number|Odious]] |
+ | * [[Pernicious number|Pernicious]] | ||
+ | |||
+ | |group15 = Generated via a [[Sieve theory|sieve]] | ||
+ | |list15 = | ||
+ | * [[Lucky number|Lucky]] | ||
+ | * [[Generation of primes|Prime]] | ||
+ | |||
+ | |group16 = [[Sorting algorithm|Sorting]] related | ||
+ | |list16 = | ||
+ | * [[Pancake sorting|Pancake number]] | ||
+ | * [[Sorting number]] | ||
+ | |||
+ | |group17 = [[Natural language]] related | ||
+ | |list17 = | ||
+ | * [[Aronson's sequence]] | ||
+ | * [[Ban number|Ban]] | ||
− | | | + | |group18 = [[Graphemics]] related |
− | | | + | |list18 = |
− | * [[ | + | * [[Strobogrammatic number|Strobogrammatic]] |
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− | | | + | | belowclass = hlist |
− | | | + | | belowstyle = font-weight:bold; |
− | + | | below = | |
− | + | * {{icon|Portal}} [[Portal:Mathematics|Mathematics portal]] | |
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}}<noinclude> | }}<noinclude> | ||
+ | {{documentation|content= | ||
{{collapsible option}} | {{collapsible option}} | ||
− | [[Category:Mathematics | + | ==See also== |
+ | *{{tl|Divisor classes}} | ||
+ | *{{tl|Figurate numbers}} | ||
+ | *{{tl|Prime number classes}} | ||
+ | *{{tl|Series (mathematics)}} | ||
+ | |||
+ | [[Category:Mathematics navigational boxes]] | ||
+ | }} | ||
</noinclude> | </noinclude> |
Latest revision as of 15:52, 8 September 2020

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