Möbius Inversion Formula

A function that takes a positive integer as input and returns 1 if the integer is square-free, -1 if the integer has an even number of prime factors, and 0 otherwise.

A function that takes a positive integer as input and returns the number of prime factors of the integer.

A function that takes a positive integer as input and returns the sum of the digits of the integer.

A function that takes a positive integer as input and returns the greatest common divisor of the integer and 10.