The number of distinct prime factors of a number is denoted . The first few values for , 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). The first few values of the
Summatory 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,

**References**

Hardy, G. H. and Wright, E. M. ``The Number of Prime Factors of '' 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.

Sloane, N. J. A. Sequences
A013939 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.

© 1996-9

1999-05-24