##  [Möbius Inversion Formula](/mobius-inversion-formula) 

  ##  [Möbius Inversion Formula](https://mathlogic.quantumdictionary.io/mobius-inversion-formula-0) 

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An identity that inverts cumulative sums over divisors (or more generally over a locally finite poset) using the Möbius function of the divisor lattice or incidence algebra, allowing recovery of an arithmetic or incidence-function from its divisor-sum transform.

 

 

 

 

 





 

 



 ##  [Möbius Inversion Formula](https://puremath.quantumdictionary.io/mobius-inversion-formula-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An explicit inversion formula on the divisor poset that uses the arithmetic Möbius function μ to recover an arithmetic function from its Dirichlet convolution or from its summatory values: if F(n)=∑_{d|n} f(d) then f(n)=∑_{d|n} μ(d)F(n/d).