primePowerFormula
P43787
predicate
Indicates that a value is computed using a formula specifically involving powers of prime numbers.
All labels observed (4)
| Label | Occurrences |
|---|---|
| primePowerFormula canonical | 2 |
| primePowerFactorization | 1 |
| recurrencePrimePowers | 1 |
| valueAtPrimeSquare | 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: primePowerFormula
Generated description
Indicates that a value is computed using a formula specifically involving powers of prime numbers.
Sample triples (5)
| Subject | Object |
|---|---|
| Euler’s totient function φ(n) | φ(p^k) = p^k − p^{k−1} for prime p and integer k ≥ 1 ⓘ |
| Jordan’s totient functions | J_k(p^a) = p^{ak} - p^{(a-1)k} ⓘ |
| Jordan’s totient functions | J_k(n) = n^k ∏_{p|n}(1 - p^{-k}) via predicate surface "primePowerFactorization" ⓘ |
| Jordan’s totient functions | J_k(p^2) = p^{2k} - p^k via predicate surface "valueAtPrimeSquare" ⓘ |
| Ramanujan tau function | τ(p^{k+1}) = τ(p)τ(p^k) - p^{11}τ(p^{k-1}) for prime p and k ≥ 1 via predicate surface "recurrencePrimePowers" ⓘ |