arithmetical function
C24992
concept
An arithmetical function is a function defined on the positive integers that assigns to each integer a (usually complex or real) value, often encoding number-theoretic properties such as divisors, primes, or multiplicative structure.
All labels observed (8)
| Label | Occurrences |
|---|---|
| arithmetical function canonical | 3 |
| Chebyshev function | 2 |
| Fourier coefficient function | 1 |
| arithmetic object | 1 |
| completely multiplicative function | 1 |
| computable function | 1 |
| family of arithmetic functions | 1 |
| number-theoretic functions | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: arithmetical function
Generated description
An arithmetical function is a function defined on the positive integers that assigns to each integer a (usually complex or real) value, often encoding number-theoretic properties such as divisors, primes, or multiplicative structure.
Instances (9)
| Instance | Via concept surface |
|---|---|
| Hasse–Weil zeta function | — |
| Ackermann function | computable function |
| Jordan’s totient functions | family of arithmetic functions |
|
Chebyshev function θ(x)
linked to:
Chebyshev functions
|
Chebyshev function |
| Ramanujan tau function | Fourier coefficient function |
| Ramanujan’s sum | — |
| Liouville function | completely multiplicative function |
| Frobenius element | arithmetic object |
|
Mertens function
linked to:
Mertens
|
— |