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A332334 Let a(1) = a(2) = 1, and for n > 2 let a(n) = p where p is the largest prime such that p# divides phi(n), where phi is Euler's totient function and # is the primorial. 0

%I

%S 1,1,2,2,2,2,3,2,3,2,2,2,3,3,2,2,2,3,3,2,3,2,2,2,2,3,3,3,2,2,5,2,2,2,

%T 3,3,3,3,3,2,2,3,3,2,3,2,2,2,3,2,2,3,2,3,2,3,3,2,2,2,5,5,3,2,3,2,3,2,

%U 2,3,2,3,3,3,2,3,5,3,3,2,3,2,2,3,2,3,2

%N Let a(1) = a(2) = 1, and for n > 2 let a(n) = p where p is the largest prime such that p# divides phi(n), where phi is Euler's totient function and # is the primorial.

%C Pollack and Pomerance show that the normal order of a(n) is log log n/log log log n. The maximal order is log n (for primorial primes A018239, by the prime number theorem) and the minimal order, for n > 2, is 2 (for products of Fermat primes A143512, apart from 1).

%H Paul Pollack and Carl Pomerance, <a href="https://arxiv.org/abs/2001.06727">Phi, primorials, and Poisson</a>, arXiv:2001.06727 [math.NT], 2020.

%o (PARI) a(n)=my(ph=eulerphi(n)); my(p=1); forprime(q=2,, if(ph%q, return(p), p=q))

%Y Cf. A018239, A143512.

%K nonn

%O 1,3

%A _Charles R Greathouse IV_, Feb 09 2020

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Last modified October 28 17:59 EDT 2021. Contains 348329 sequences. (Running on oeis4.)