##  [Sigma Function](/sigma-function) 

  ##  [Sigma Function](https://puremath.quantumdictionary.io/sigma-function-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Family of arithmetic functions σ_k(n) = ∑_{d|n} d^k that sum the k-th powers of positive divisors of n; the common special cases are σ_0(n)=d(n) (number of divisors) and σ_1(n)=σ(n) (sum of divisors).