where the Möbius function μ is defined as follows: let a natural number n to be written as a multiplication of primes:

Then μ(n) = (-1)^{r} where k_{1}= .....=k_{r}=1; μ(1) = 1; μ(n) = 0 otherwise.

It follows that μ = -1 for each prime. This extraordinary function is used in the Prime Number Theorem.