How this calculation works
The value for 12 is zero because 4 divides it. A single repeated prime factor is enough to make the value zero.
THE FORMULA
μ(n) = 0 if a prime square divides n, otherwise (−1)ᵏA worked example
30 = 2 × 3 × 5 has three distinct primes, so μ(30) = −1.
Good to know
By convention μ(1) = 1.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Evaluate the Möbius function from prime multiplicities.
The primary result is labeled “μ(n)”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
By convention μ(1) = 1.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
30 = 2 × 3 × 5 has three distinct primes, so μ(30) = −1.
Which rule does this calculator apply?
μ(n) = 0 if a prime square divides n, otherwise (−1)ᵏ