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.
- Ringoid
- Ring Torus
- Risch Algorithm
- Rising Factorial
- Rivest-Shamir-Adleman Number
- RMS
- r(n)
- Robbin Constant
- Robbins Algebra
- Robbins Equation
- Robbin's Inequality
- Robertson Condition
- Robertson Conjecture
- Robertson-Seymour Theorem
- Robin Boundary Conditions
- Robin's Constant
- Robinson Projection
- Robust Estimation
- Rodrigues Formula
- Rodrigues's Curvature Formula
- Rogers-Ramanujan Continued Fraction
- Rogers-Ramanujan Identities
- Rolle's Theorem
- Roman Coefficient
- Roman Factorial