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: The apparently vague definition given by Hardy and Wright and mentioned in the first line of the article becomes clear in view of the classical functions they consider in their chapter 16. A more precise and less restrictive definition is however widely accepted by number theorists:
:"An arithmetic function is any real- or complex-valued function defined on the set N of positive integers. (In other words, an arithmetic function is just a sequence of real or complex numbers, though this point of view is not particularly useful)", see [http://www.math.illinois.edu/~ajh/ant/main1.pdf].[[User:Sapphorain|Sapphorain]] ([[User talk:Sapphorain|talk]]) 08:15, 8 June 2017 (UTC)
:: ... I added three classical references giving this less restrictive definition, and modified the lead accordingly. [[User:Sapphorain|Sapphorain]] ([[User talk:Sapphorain|talk]]) 15:41, 8 June 2017 (UTC)
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