In number theory, the **normal order** of an arithmetic function describes the typical or average asymptotic behavior of the function across integers. More formally, an arithmetic function \( f(n) \) is said to have a normal order \( g(n) \) if, for almost all integers \( n \), \( f(n) \) is approximately equal to \( g(n) \) in a certain sense.
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A positive function is a normal order of an arithmetic function when, for every , all but integers satisfy .