Completely multiplicative function: Difference between revisions

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*#REDIRECT [[Multiplicative function]]

:''Outside number theory, the term '''multiplicative''' is usually used for functions with this property.''

An arithmetic function ''f''(''n'') is said to be '''completely multiplicative''' (or '''totally multiplicative''') if ''f''(1) = 1 and ''f''(''ab'') = ''f''(''a'') ''f''(''b'') holds ''for all'' positive integers ''a'' and ''b''.

This requires either ''f''(1) = 1, or ''f''(''a'') = 0 for all ''a'' except ''a'' = 1.

==See also==

*[[Multiplicative function]]

[[Category:Multiplicative functions]]

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