

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



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, 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, 2, 3, 2, 3, 3, 3, 2, 3, 5, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2
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OFFSET

1,3


COMMENTS

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).


LINKS

Table of n, a(n) for n=1..87.
Paul Pollack and Carl Pomerance, Phi, primorials, and Poisson, arXiv:2001.06727 [math.NT], 2020.


PROG

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


CROSSREFS

Cf. A018239, A143512.
Sequence in context: A338094 A165035 A236531 * A217403 A081309 A329377
Adjacent sequences: A332331 A332332 A332333 * A332335 A332336 A332337


KEYWORD

nonn


AUTHOR

Charles R Greathouse IV, Feb 09 2020


STATUS

approved



