special functions - What are the terms of the sequence generated by Zeta(3s)/Zeta(s)?

The LiouvilleLambda function has Dirichlet generating function of Zeta[2s]/Zeta[s]. I am curious about an analogous function with Dirichlet generating function of Zeta[3s]/Zeta[s].

Can Mathematica return the first few terms of such a sequence?

I am most interested in a code that is simple to understand. I am not concerned about efficiency.