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In number theory, a normal order of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate values. Let ƒ be a function on the natural numbers. We say that ''g'' is a normal order of ƒ if for every ''ε'' > 0, the inequalities : hold for ''almost all'' ''n'': that is, if the proportion of ''n'' ≤ ''x'' for which this does not hold tends to 0 as ''x'' tends to infinity. It is conventional to assume that the approximating function ''g'' is continuous and monotone. ==Examples== * The Hardy–Ramanujan theorem: the normal order of ω(''n''), the number of distinct prime factors of ''n'', is log(log(''n'')); * The normal order of Ω(''n''), the number of prime factors of ''n'' counted with multiplicity, is log(log(''n'')); * The normal order of log(''d''(''n'')), where ''d''(''n'') is the number of divisors of ''n'', is log(2) log(log(''n'')). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「normal order of an arithmetic function」の詳細全文を読む スポンサード リンク
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