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Reference.org
Additive function
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<p>In <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, an additive function is an <a href="/facts/Arithmetic_function/hULxwsgm">arithmetic function</a> <i>f</i>(<i>n</i>) of the positive <a href="/facts/Integer/PUwwrawx">integer</a> variable <i>n</i> such that whenever <i>a</i> and <i>b</i> are <a href="/facts/Coprime/bnCxCXxs">coprime</a>, the function applied to the product <i>ab</i> is the sum of the values of the function applied to <i>a</i> and <i>b</i>: f ( a b ) = f ( a ) + f ( b ) . {\displaystyle f(ab)=f(a)+f(b).} </p>