Summing : a faster elementary algorithm.

We present a new elementary algorithm that takes (measured bitwise) for computing where is the Möbius function. This is the first improvement in the exponent of for an elementary algorithm since 1985. We also show that it is possible to reduce space consumption to by the use of (Helfgott in: Math Comput 89:333-350, 2020), at the cost of letting time rise to the order of .