Divisors of a natural number
Builds on Divisibility
Definition
Let be a positive integer. The set of divisors of is the set of positive integers that divide :
Remarks
The set is finite, because each satisfies . It always contains and . For example, . The map is a bijection from to itself. Sums over define the divisor function and the Dirichlet convolution.
Reading path
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- Divisibility definition
- Divisors of a natural number definition
Where this leads
14 pages build on this one.
- Sum of divisors
- Multiplicativity of the divisor function
- Möbius inversion formula
- The Möbius function is the inverse of the constant function 1
- Number of divisors
- Deficient number
- Dirichlet convolution
- Dirichlet convolution of multiplicative functions is multiplicative
- Dirichlet convolution formula
- Perfect number
- Abundant number
- Euclid–Euler theorem
- Divisor function
- Lambert series
Further reading
- Web https://en.wikipedia.org/wiki/Divisor, Definition
About this page
| Tag | 0FCWA16FZE |
|---|---|
| URI | m2://0FCWA16FZE |
| Kind | definition |
| Writing | W0 stub |
| MSC | 11A05 |
| Defines | Divisors of a natural number |
| Uses | Divisibility |
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