In mathematics, the classic Möbius inversion formula was introduced into number theory during the 19th century by August Ferdinand Möbius.
Other Möbius inversion formulas are obtained when different locally finite partially ordered sets replace the classic case of the natural numbers ordered by divisibility; for an account of those, see incidence algebra.
![F(n) = \sum_{d|n} f(d)](/Images/godic/202501/27/536fd7c4ce550e9c2e51c6f50211c1ae4523.png")
![f(n) = \sum_{d|n} \mu (d) F \left( \frac{n}{d} \right)](/Images/godic/202501/27/57445f1c4deac141b0611e4c6053ac7f4523.png")