Mobius Function Calculator

This Mobius function calculator works out mu(n) for any whole number you enter, a value central to number theory that links directly to prime factorisation. Enter n as a whole number from 1 up to one billion, and the calculator returns mu(n) itself, whether n is squarefree, and the count of its distinct prime factors, so you can see exactly how the result was reached. The Mobius function follows a simple three-way rule: mu(1) equals 1; mu(n) equals 0 whenever n is divisible by the square of any prime; and for every other, squarefree, number, mu(n) is plus 1 if it has an even number of distinct prime factors and minus 1 if it has an odd number. Type in any number, whether a small textbook example or a large value with several prime factors, and the tool factorises it instantly rather than making you work through the arithmetic by hand. This makes it useful for students checking homework, programmers testing number-theory code, and anyone exploring how the Mobius function underpins Mobius inversion, counting arguments in combinatorics, and the deep connection between the primes and the Riemann zeta function. A worked example below shows how 30 and 12 give different results, one squarefree and one not, so you can confirm the calculator matches the definition before relying on it for your own numbers.

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