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
where
is a Landau symbol.
The theorem is discussed in Kac (1959).
See also
Distinct Prime Factors,
Hardy-Ramanujan Theorem
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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.Referenced on Wolfram|Alpha
Erdős-Kac Theorem
Cite this as:
Weisstein, Eric W. "Erdős-Kac Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Erdos-KacTheorem.html
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