:Template:Classes of natural numbers/sandbox
{{Navbox
| name = Classes of natural numbers
| title = Classes of natural numbers
| listclass = hlist
| state = {{{state|
|group1 = Powers and
related numbers
|list1 =
- Achilles numbers
- Powers of two
- Powers of 10
- Squares
- Cubes
- Fourth powers
- Fifth powers
- Perfect powers
- Powerful numbers
- Prime powers
|group2 = Of the form
a × 2b ± 1
|list2 =
- Cullen numbers
- Double Mersenne numbers
- Fermat numbers
- Mersenne numbers
- Proth numbers
- Thabit numbers
- Woodall numbers
|group3 = other polynomial
numbers
|list3 =
- Carol numbers
- Hilbert numbers
- Idoneal numbers
- Kynea numbers
- Leyland numbers
- Lucky numbers of Euler
|group4 = Recursively defined
numbers
|list4 =
|group5 = Possessing a
specific set
of other numbers
|list5 =
|group6 = Expressible via
specific sums
|list6 =
- Nonhypotenuse numbers
- Polite numbers
- Practical numbers
- Primary pseudoperfect numbers
- Ulam numbers
- Wolstenholme numbers
|group7 = Generated
via a sieve
|list7 =
|group8 = Code related
|list8 =
|group9 =
|list9 =
|group10 = Pseudoprimes
|list10 =
- Carmichael numbers
- Catalan pseudoprimes
- Elliptic pseudoprimes
- Euler pseudoprimes
- Euler–Jacobi pseudoprimes
- Fermat pseudoprimes
- Fibonacci pseudoprimes
- Frobenius pseudoprimes
- Lucas pseudoprimes
- Somer–Lucas pseudoprimes
- Strong pseudoprimes
|group11 = Combinatorial
numbers
|list11 =
- Bell numbers
- Cake numbers
- Catalan numbers
- Dedekind numbers
- Delannoy numbers
- Lazy caterer's sequence
- Lobb numbers
- Motzkin numbers
- Narayana numbers
- Ordered Bell numbers
- Schröder numbers
- Schröder–Hipparchus numbers
|group12 = Arithmetic functions
|list12 = {{Navbox|subgroup
|group1 = By properties of σ(n)
|list1 =
- Abundant numbers
- Almost perfect numbers
- Arithmetic numbers
- Colossally abundant numbers
- Descartes numbers
- Hemiperfect numbers
- Highly abundant numbers
- Hyperperfect numbers
- Multiply perfect numbers
- Perfect numbers
- Primitive abundant numbers
- Quasiperfect numbers
- Refactorable numbers
- Sublime numbers
- Superabundant numbers
- Superior highly composite numbers
- Superperfect numbers
|group2 = By properties of Ω(n)
|list2 =
|group3 = By properties of φ(n)
|list3 =
- Highly cototient numbers
- Highly totient numbers
- Noncototients
- Nontotients
- Perfect totient numbers
- Sparsely totient numbers
|group4 = By properties of s(n)
|list4 =
}}
|group13 = Dividing a quotient
|list13 =
|group14 = Other prime factor
or divisor related
numbers
|list14 =
- Blum integers
- Erdős–Woods numbers
- Friendly numbers
- Frugal numbers
- Giuga numbers
- Harmonic divisor numbers
- Highly composite numbers
- Lucas–Carmichael numbers
- Pronic numbers
- Regular numbers
- Rough numbers
- Smooth numbers
- Sociable numbers
- Sphenic numbers
- Størmer numbers
- Super-Poulet numbers
|group15 = Base-dependent
numbers
|list15 =
- Automorphic numbers
- Dudeney numbers
- Equidigital numbers
- Extravagant numbers
- Factorions
- Friedman numbers
- Happy numbers
- Harshad numbers
- Kaprekar numbers
- Keith numbers
- Lychrel numbers
- Palindromic numbers
- Pandigital numbers
- Parasitic numbers
- Polydivisible numbers
- Primeval numbers
- Repdigits
- Repunits
- Self numbers
- Self-descriptive numbers
- Smarandache–Wellin numbers
- Strobogrammatic numbers
- Sum-product numbers
- Transposable integers
- Trimorphic numbers
- Undulating numbers
- Vampire numbers
|group16 = Recreational
mathematics
|list16 =
|group17 =
|list17 = {{Figurate numbers|border=subgroup}}
}}
{{collapsible option}}