Arithmetic function
Definition
An arithmetic function is a function from the positive integers to the complex numbers.
Remarks
Examples are Euler's totient function , the divisor function and the Möbius function . Some texts allow values in another commutative ring, or set and use all natural numbers as the domain. The Dirichlet convolution makes the arithmetic functions into a commutative ring.
Where this leads
23 pages build on this one.
- Sum of divisors
- Multiplicativity of the divisor function
- Möbius inversion formula
- Number of prime factors counted with multiplicity
- Liouville function
- Multiplicative function
- The Möbius function is the inverse of the constant function 1
- Number of divisors
- Möbius function
- Deficient number
- Completely multiplicative function
- Dirichlet convolution
- Dirichlet convolution of multiplicative functions is multiplicative
- Dirichlet convolution formula
- Perfect number
- Multiplicativity of the Möbius function
- Abundant number
- Euclid–Euler theorem
- Divisor function
- Number of distinct prime factors
- Lambert series
- Euler product for multiplicative functions
- Lambert summation
Further reading
- Web https://en.wikipedia.org/wiki/Arithmetic_function, lead section
About this page
| Tag | 0H2EPRZC0D |
|---|---|
| URI | m2://0H2EPRZC0D |
| Aliases | arithmetical-function, number-theoretic-function |
| Kind | definition |
| Writing | W1 stated |
| MSC | 11A25 |
| Defines | Arithmetic function |
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What this page needs for W2
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