The paper proves the following theorem: let $f(n)$ multiplicative function satisfying the following system of functional equations \[ f(n)^2=um_{d|n}\mu^2(d)f\Big(\frac nd\Big)iF^2(n)=um_{d|n}f(d^2) \] when is a) $f(n)=0$ or b) $f(n)=\tau(n)$ (nuber of dividers $n$) or c) $f(n)$ generated with $\frac{\zeta(3s)}{\zeta(s)}$, i.e., $\sum_{n=1}^{\infty}f(n)n^{-s}=\frac{\zeta(3s)}{\zeta(s)}$.