The function named after this man is equal to zero for non square-free numbers, one for numbers with an even number of prime factors and negative one for numbers with an odd number of prime factors. A statement involving summing over divisors that uses the aforementioned function is his namesake inversion formula. The orientability of a surface is determined by whether it contains a subset homeomorphic to an entity named after this man, which when glued to itself forms a Klein bottle. For 10 points, identify this man who names an object that has only one side which is 
The function named after this man is equal to zero for non square-free numbers, one for numbers with an even number of prime factors and negative one for numbers with an odd number of prime factors. A statement involving summing over divisors that uses the aforementioned function is his namesake inversion formula. The orientability of a surface is determined by whether it contains a subset homeomorphic to an entity named after this man, which when glued to itself forms a Klein bottle. For 10 points, identify this man who names an object that has only one side which is formed by taking a piece of paper, twisting it, and then gluing the ends together, his namesake strip.
The function named after this man is equal to zero for non square-free numbers, one for numbers with an even number of prime factors and negative one for numbers with an odd number of prime factors.
August (Ferdinand) Mobius