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Completely multiplicative function
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<p>In <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, functions of <a href="/facts/Positive_integer/u65og8JE">positive integers</a> which respect products are important and are called completely multiplicative functions or totally multiplicative functions. A weaker condition is also important, respecting only products of <a href="/facts/Coprime/bnCxCXxs">coprime</a> numbers, and such functions are called <a href="/facts/Multiplicative_function/4kfolbBl">multiplicative functions</a>. Outside of number theory, the term "multiplicative function" is often taken to be synonymous with "completely multiplicative function" as defined in this article. </p>