Editing Additive function (section)

{{Short description|Function that can be written as a sum over prime factors}}
{{About||the [[Abstract algebra|algebra]]ic meaning|Additive map}}
{{more footnotes|date=February 2013}}

In [[number theory]], an '''{{anchor|definition-additive_function-number_theory}}additive function''' is an [[arithmetic function]] ''f''(''n'') of the positive [[integer]] variable ''n'' such that whenever ''a'' and ''b'' are [[coprime]], the function applied to the product ''ab'' is the sum of the values of the function applied to ''a'' and ''b'':<ref name="Erdos1939">Erdös, P., and M. Kac. On the Gaussian Law of Errors in the Theory of Additive Functions. Proc Natl Acad Sci USA. 1939 April; 25(4): 206–207. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1077746/ online]</ref>
<math display=block>f(a b) = f(a) + f(b).</math>