| The {\em 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 $\Omega(n)$ is an additive function. |
The {\em 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 $\Omega(n)$ is an additive function. |
