Mertens function

In number theory, the Mertens function is defined for all positive integers n as where μ(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: Less formally, is the count of square-free integers up to x that have an even number of prime factors, minus the count of those that have an odd number. The first 143 M(n) is: (sequence in the OEIS) The true rate of growth of M(x) is not known. An unpublished conjecture of Steve Gonek states that

Mertens function

In number theory, the Mertens function is defined for all positive integers n as where μ(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: Less formally, is the count of square-free integers up to x that have an even number of prime factors, minus the count of those that have an odd number. The first 143 M(n) is: (sequence in the OEIS) The true rate of growth of M(x) is not known. An unpublished conjecture of Steve Gonek states that