Möbius Function Calculator

μ(n) = (−1)ᵏ or 0

All Tools

μ(30) = -1

SquarefreeM(30) = -3

30 = 2 × 3 × 5

μ(k) & M(k)

1: +1

2: -1

3: -1

4: 0

5: -1

6: +1

7: -1

8: 0

9: 0

10: +1

11: -1

12: 0

13: -1

14: +1

15: +1

16: 0

17: -1

18: 0

19: -1

20: 0

21: +1

22: +1

23: -1

24: 0

25: 0

26: +1

27: 0

28: 0

29: -1

30: -1

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About Möbius Function Calculator

A Möbius function calculator computing μ(n): 1 if n=1, 0 if n has a squared factor, (−1)ᵏ if n is product of k distinct primes. Shows prime factorization and Möbius inversion. All calculations are client-side.

Möbius Function Calculator Features

μ(n)
Factorization
Squarefree check
Table
Mertens function

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