The nth Mobius number is given by the piecewise function:

       /  0      if n has any repeated factors
       |
       /
u(n) = |  1      if n=1
       \
       |      k
       \  (-1)   if n is a product of k distinct primes

The first several values of u(n) (n=1,2,3,...) are u(n)=1, -1, -1, 0, -1, 1, ... Mobius numbers are multiplicative, i.e.:

         /  u(m)*u(n)  if gcd(m,n)=1
u(m*n) = |
         \  0          otherwise

All information gathered from http://mathworld.wolfram.com/MoebiusFunction.html