Möbius Function Calculator
Möbius μ(n): 0 when divisible by a square, (−1)^k with k distinct primes, μ(1)=1.
Description
Möbius μ(n): 0 when divisible by a square, (−1)^k with k distinct primes, μ(1)=1.
Möbius μ(n): 0 when divisible by a square, (−1)^k with k distinct primes, μ(1)=1.
When to use Möbius Function Calculator
Use this tool to test or transform exact integers according to the named number-theory definition, for education, validation, or algorithm checks.
- n
- Positive integer.
How the calculation works
The formula below determines the tool output. μ(n): −1, 0, or 1.1
μ(n) = 0 for a squared prime factor; otherwise μ(n) = (−1)^k Limitations and assumptions
This tool applies an exact integer definition within JavaScript's safe-integer range. It is not an arbitrary-precision factorization or proof system, so do not use rounded measurements or integers beyond the accepted domain as though they were exact.
Alternative or Complementary approaches
Complement a number-property result with its factorization, divisors, digit representation, or a second independent predicate. A true result establishes only the named property and does not imply other properties such as primality.
References
-
Möbius function — Wikipedia contributors
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