So I believe you are asking about the Moebius or Möbius Mu(n) function. This is a number theoretic function defined as follows:

Mu(n) = 0 if n has one or more repeated prime factors Mu(n) = 1 if n = 1 Mu(n) = (−1)^k if n is the product of k distinct primes Mu(n) = Mu(−n), (Mu(n) is not normally defined for n < 1) Mu(0) = 0

So the answer to your question is mu of zero is 0

Dr. Chuck

However, if you are looking for the value of mu subscript 0, μ₀ that equals 4(pi) x 10^-7 T m/A

μ₀ = 4π x 10^-7 T m/A