cp's OEIS Frontend

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.

%I A332334 #8 Feb 10 2020 02:23:24
%S A332334 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 A332334 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 A332334 2,3,2,3,3,3,2,3,5,3,3,2,3,2,2,3,2,3,2
%N 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.
%C A332334 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 A332334 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 A332334 (PARI) a(n)=my(ph=eulerphi(n)); my(p=1); forprime(q=2,, if(ph%q, return(p), p=q))
%Y A332334 Cf. A018239, A143512.
%K A332334 nonn
%O A332334 1,3
%A A332334 _Charles R Greathouse IV_, Feb 09 2020