Möbius function

discrete curve

h12mobif.gif (1245 bytes)

where the Möbius function μ is defined as follows:
h12mobi.gif (2313 bytes)let a natural number n to be written as a multiplication of primes:

h12mobig.gif (1021 bytes)

Then μ(n) = (-1)r where k1= .....=kr=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.