##  [Chebyshev Psi Function](/chebyshev-psi-function) 

  ##  [Chebyshev Psi Function](https://puremath.quantumdictionary.io/chebyshev-psi-function-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Summatory arithmetic function ψ(x)=Σ_{n≤x}Λ(n)=Σ_{p^k≤x}log p that sums log p over all prime powers p^k not exceeding x; it counts primes with multiplicity according to their prime-power contributions.