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Line 2: ==Definition== A '''completely multiplicative function''' (or '''totally multiplicative function''') is an [[arithmetic function]] (that is, a function whose [[Domain ~~(mathematics)~~of a function\|___domain]] is the [[natural number]]s), such that ''f''(1) = 1 and ''f''(''ab'') = ''f''(''a'')''f''(''b'') holds ''for all'' positive integers ''a'' and ''b''.<ref>{{cite book\|last=Apostol\|first=Tom\|title=Introduction to Analytic Number Theory\|year=1976\|publisher=Springer\|isbn=0-387-90163-9\|pages=[https://archive.org/details/introductiontoan00apos_0/page/30 30]\|url-access=registration\|url=https://archive.org/details/introductiontoan00apos_0/page/30}}</ref> Without the requirement that ''f''(1) = 1, one could still have ''f''(1) = 0, but then ''f''(''a'') = 0 for all positive integers ''a'', so this is not a very strong restriction.

Completely multiplicative function: Difference between revisions