Prime Factors

The number of Distinct Prime Factors of a number $n$ is denoted $\omega(n)$. The first few values for $n=1$, 2, ... are 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, ... (Sloane's A001221; top figure). The number of not necessarily distinct prime factors of a number $n$ is denoted $r(n)$. The first few values for $n=1$, 2, ... are 0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, ... (Sloane's A001222; bottom figure).

See also Distinct Prime Factors, Divisor Function, Greatest Prime Factor, Least Prime Factor, Liouville Function, Pólya Conjecture, Prime Factorization Algorithms

References

Sloane, N. J. A. Sequences A001222/M0094 and A001221/M0056 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.