In number theory, the Erdős arcsine law, named after Paul Erdős in 1969, states that the prime divisors of a number have a distribution related to the arcsine distribution.
Specifically, say that the th prime factor of a given number (in the sorted sequence of distinct prime factors) is "small" when . Then, for any fixed parameter , in the limit as goes to infinity, the proportion of the integers less than that have fewer than small prime factors converges to
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