#### Abstract

Let ω(n) and Ω(n) denote the number of prime factors of n, counted without multiplicity and with multiplicity, respectively. In 1917, Hardy and Ramanujan [7] proved that the normal order of ω(n) and Ω(n) is log log n. This means that given any > 0, the number of n ≤ x failing to satisfy the inequality | f (n) − log log n| < log log n, with f = ω or Ω, is o… (More)

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