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Prime FactorsThe 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; top figure). Thenumber of not necessarily distinct prime factors of a number is denoted . The first few values for ,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. SequencesA001222/M0094and A001221/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.
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