Let n = p
2 … pr
be a product of r prime numbers which are not necessarily different. We define then an arithmetic function µm
where m is a natural number. We further define the function L(s, µ
) by the Dirichlet series
and will show that L(s, µm
), (m ≥ 3), has an infinitely many valued analytic continuation into the half plane Re s > ½.