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

Author

Charles R Greathouse IV, Feb 09 2020

Keywords

• nonn

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

• Paul Pollack and Carl Pomerance, Phi, primorials, and Poisson, arXiv:2001.06727 [math.NT], 2020.

Crossrefs

Cf. A018239, A143512.

Programs

PARI

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