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Line 12: Arithmetic functions which are completely additive are: * The restriction of the [[logarithm\|logarithmic function]] to '''N'''. * The function Ω(''n''), defined as the total number of [[prime number\|prime]] factors of ''n'', counting multiple factors multiple times. This implies Ω(1) = 0 since 1 has no prime factors. Some values: ([http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001222 SIDN A001222]) ::Ω(4) = 2 Line 26: :: ... An example of an arithmetic function which is additive but not completely additive is ω(''n''), defined as the total number of ''different'' [[prime number\|prime]] factors of ''n''. Some values (compare with Ω(''n'')) ([http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001221 SIDN A001221]) : ::ω(4) = 1

Additive function: Difference between revisions