For arithmetic functions: if g(n) = Σ_{d|n} f(d) then f(n) = Σ_{d|n} μ(n/d) g(d), where μ is the Möbius function (μ(1)=1, μ(squarefree with k prime factors)=(−1)^k, 0 otherwise). Gauss identity Σ_{d|n} φ(d) = n follows; generalises to…
For arithmetic functions: if g(n) = Σ_{d|n} f(d) then f(n) = Σ_{d|n} μ(n/d) g(d), where μ is the Möbius function (μ(1)=1, μ(squarefree with k prime factors)=(−1)^k, 0 otherwise). Gauss identity Σ_{d|n} φ(d) = n follows; generalises to…