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Arithmetic function
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== Multiplicative and additive functions == An arithmetic function ''a'' is * '''[[Completely additive function|completely additive]]''' if ''a''(''mn'') = ''a''(''m'') + ''a''(''n'') for all natural numbers ''m'' and ''n''; * '''[[Completely multiplicative function|completely multiplicative]]''' if ''a''(1) = 1 and ''a''(''mn'') = ''a''(''m'')''a''(''n'') for all natural numbers ''m'' and ''n''; Two whole numbers ''m'' and ''n'' are called [[coprime]] if their [[greatest common divisor]] is 1, that is, if there is no [[prime number]] that divides both of them. Then an arithmetic function ''a'' is * '''[[Additive function|additive]]''' if ''a''(''mn'') = ''a''(''m'') + ''a''(''n'') for all coprime natural numbers ''m'' and ''n''; * '''[[Multiplicative function|multiplicative]]''' if ''a''(1) = 1 and ''a''(''mn'') = ''a''(''m'')''a''(''n'') for all coprime natural numbers ''m'' and ''n''.
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