Given a positive integer $n$, are there estimates for the sum of distinct prime factors of $n$ and for the number of distinct prime factors of $n$ (sometimes denoted $\omega(n)$)? I'm not interested in asymptotics, but it would be useful to have some inequalities for each $n$.
- number of distinct prime factors: http://oeis.org/A001221
- sum of distinct prime factors: http://oeis.org/A008472