Problems including the Liouville function, $\lambda(n)$, which is equal to $(-1)^k$, where $k$ is the number of prime factors of $n$ (with multiplicity).
The Liouville function $\lambda(n)$ is defined for positive integers $n$ using their prime factorization. We have $\lambda(1)=1$ and otherwise if $n=p_1^{a_1}\cdots p_r^{a_r}$, then $\lambda(n)=(-1)^r$.
The Lioville function is totally multiplicative: if $m$ and $n$ are relatively prime, then
$$\lambda(mn) = \lambda(m) \lambda(n).$$
For $\Re(s)>1$, its Dirichlet series is $$ \sum_{n=1}^{\infty} \frac{\lambda(n)}{n^s} = \frac{\zeta(2s)}{\zeta(s)} $$
