Abstract:This article deals with the value distribution of multiplicative prime-independent arithmetic functions $(\alpha (n))$ with $\alpha (n)=1$ if $n$ is $N$-free ($N\ge 2$ a fixed integer), $\alpha (n)>1$ else, and $\alpha (2^n)\to \infty $. An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.
Keywords: arithmetic functions, value distribution, finite Abelian groups
AMS Subject Classification: 11N64, 11N37, 11N45