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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 17:33 EDT 2021. Contains 347716 sequences. (Running on oeis4.)