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Date: 6-9-2020
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A deeper result than the Hardy-Ramanujan theorem. Let be the number of integers in such that inequality
(1) |
holds, where is the number of distinct prime factors of . Then
(2) |
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(3) |
where is a Landau symbol.
The theorem is discussed in Kac (1959).
REFERENCES:
Kac, M. Statistical Independence in Probability, Analysis and Number Theory. New York: Wiley, 1959.
Riesel, H. "The Erdős-Kac Theorem." Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 158-159, 1994.
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