Distinct Prime Factors
The number of distinct prime factors of a number 
is denoted 
. The first few values for 
, 2, ... are0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, ... (Sloane's A001221). The first few values of theSummatory Function
are 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 17, 19, 20, 21, ... (Sloane's A013939), and the asymptotic value is
where
is Mertens Constant. In addition,
See also Divisor Function, Greatest Prime Factor, Hardy-Ramanujan Theorem, Heterogeneous Numbers,Least Prime Factor, Mertens Constant, Prime Factors
References
Hardy, G. H. and Wright, E. M. ``The Number of Prime Factors of Sloane, N. J. A. SequencesA013939 andA001221/M0056in ``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.'' and ``The Normal Order of and 
.'' §22.10 and 22.11 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 354-358, 1979.
- Cumulant
- Cumulant-Generating Function
- Cumulative Distribution Function
- Cundy and Rollett's Egg
- Cunningham Chain
- Cunningham Function
- Cunningham Number
- Cunningham Project
- Cupola
- Cupolarotunda
- Curl
- Curlicue Fractal
- Curl Theorem
- Current
- Curtate Cycloid
- Curtate Cycloid Evolute
- Curvature
- Curvature Center
- Curvature Scalar
- Curvature Vector
- Curve
- Curve of Constant Breadth
- Curve of Constant Precession
- Curve of Constant Slope
- Curve of Constant Width