The number of (nondistinct) prime factors function $\Omega(n)$ counts with repetition how many prime factors a natural number $n$ has. If $\displaystyle n= \prod_{j= 1}^k {p_j}^{a_j}$ where the $k$ primes $p_j$ are distinct and the $a_j$ are natural numbers, then $\displaystyle \Omega(n)=\sum_{j=1}^k a_j$

Note that, if $n$ is a squarefree number, then $\omega(n)=\Omega(n)$ where $\omega(n)$ is the number of distinct prime factors function. Otherwise, $\omega(n)<\Omega(n)$

Note also that $\Omega(n)$ is a completely additive function and thus can be exponentiated to define a completely multiplicative function. For example, the Liouville function can be defined as $\lambda(n) = (-1)^{\Omega(n)}$

The sequence $\{\Omega(n)\}$ appears in the OEIS as sequence A001222.

The sequence $\{2^{\Omega(n)}\}$ appears in the OEIS as sequence A061142.