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- W3001727521 abstract "The primorial p # of a prime p is the product of all primes q ≤ p . Let pr ( n ) denote the largest prime p with p # ∣ ϕ ( n ) , where ϕ is Euler’s totient function. We show that the normal order of pr ( n ) is log log n / log log log n ; that is, pr ( n ) ∼ log log n / log log log n as n → ∞ on a set of integers of asymptotic density 1. In fact, we show there is an asymptotic secondary term and, on a tertiary level, there is an asymptotic Poisson distribution. We also show an analogous result for the largest integer k with k ! ∣ ϕ ( n ) ." @default.
- W3001727521 created "2020-01-30" @default.
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- W3001727521 date "2020-09-01" @default.
- W3001727521 modified "2023-10-10" @default.
- W3001727521 title "Phi, primorials, and Poisson" @default.
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- W3001727521 doi "https://doi.org/10.1215/00192082-8591576" @default.
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