Additive function: Difference between revisions

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In [[number theory]], an '''additive function''' is an [[arithmetic function]] ''f''(''n'') of the positive [[integer]] ''n'' such that whenever ''a'' and ''b'' are [[coprime]], the function of the product is the sum of the functions:

:''f''(''ab'') = ''f''(''a'') + ''f''(''b'').

Outside number theory, the term '''additive''' may also be used for all functions with the property ''f''(''ab'') = ''f''(''a'') + ''f''(''b'') for all arguments ''a'' and ''b''.

The remainder of this article discusses number theoretic additive functions, using the second definition.