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.

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

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 A378671 A081309

Adjacent sequences: A332331 A332332 A332333 * A332335 A332336 A332337

Keyword

nonn

Author

Charles R Greathouse IV, Feb 09 2020

Status

approved