Equation that approximates the number of factors a whole number has

Question

As far as I know, there are certain equations that approximate the distribution of prime numbers based on their size. Are there similar equations that approximate the number of prime factors that a whole number will have, based on it's size or other variables?

Answer 1

The average number of prime factors of $n$ is $\ln \ln n$:

http://mathworld.wolfram.com/DistinctPrimeFactors.html

The maximum number is $\frac{\ln n}{\ln \ln n}$.

See the references in the above article, especially Hardy and Wright.