number of (nondistinct) prime factors function
The counts with repetition how many prime factors a natural number
has. If where the primes are distinct and the are natural numbers, then .
Note that, if is a squarefree number, then , where is the number of distinct prime factors function. Otherwise, .
Note also that 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 .
The sequence appears in the OEIS as sequence http://www.research.att.com/ njas/sequences/?q=A001222A001222.
The sequence appears in the OEIS (http://planetmath.org/OEIS) as sequence http://www.research.att.com/ njas/sequences/?q=A061142A061142.