DirichletConvolution
P43789
predicate
Indicates that two arithmetic functions are combined into a new function by summing the products of their values over all pairs of positive integers whose product equals a given integer.
All labels observed (3)
| Label | Occurrences |
|---|---|
| DirichletConvolution canonical | 2 |
| convolutionExplanation | 1 |
| inverseUnderDirichletConvolution | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: DirichletConvolution
Generated description
Indicates that two arithmetic functions are combined into a new function by summing the products of their values over all pairs of positive integers whose product equals a given integer.
Sample triples (4)
| Subject | Object |
|---|---|
| Euler’s totient function φ(n) | φ * 1 = id where id(n) = n ⓘ |
| Euler’s totient function φ(n) | φ = μ * id where μ is the Möbius function ⓘ |
| Jordan’s totient functions | J_k(n) = ∑_{d|n} μ(d)(n/d)^k via predicate surface "convolutionExplanation" ⓘ |
| Möbius function | constant function 1 via predicate surface "inverseUnderDirichletConvolution" ⓘ |