Möbius Inversion Formula

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.

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).