Normal Order of An Arithmetic Function - Examples

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)).

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