A068211 - OEIS

%I #26 Sep 08 2022 08:45:05

%S 2,2,2,2,3,2,3,2,5,2,3,3,2,2,2,3,3,2,3,5,11,2,5,3,3,3,7,2,5,2,5,2,3,3,

%T 3,3,3,2,5,3,7,5,3,11,23,2,7,5,2,3,13,3,5,3,3,7,29,2,5,5,3,2,3,5,11,2,

%U 11,3,7,3,3,3,5,3,5,3,13,2,3,5,41,3,2,7,7,5,11,3,3,11,5,23,3,2,3,7,5,5

%N Largest prime factor of Euler totient function phi(n).

%C Smallest numbers m, such that largest prime factor of phi(m) is prime(n), a(n) is a prime number and identical to the n-th term of A035095: min{x: A068211(x) = prime(n)} = A035095(n). E.g., phi(A035095(7)) = phi(103) = 2*3*17 of which 17 = prime(7) is the largest prime factor.

%H T. D. Noe, <a href="/A068211/b068211.txt">Table of n, a(n) for n = 3..1000</a>

%F a(n) = A006530(A000010(n)).

%e For n=46, phi(46) = 2*2*11, hence a(46) = 11.

%t Table[FactorInteger[EulerPhi[n]][[-1, 1]], {n, 3, 100}] (* _Vincenzo Librandi_, Jan 04 2017 *)

%o (Magma) [Maximum(PrimeDivisors(EulerPhi(n))): n in [3..90]]; // _Vincenzo Librandi_, Jan 04 2017

%o (PARI) a(n) = vecmax(factor(eulerphi(n))[,1]); \\ _Michel Marcus_, Jan 04 2017

%Y Cf. A000010, A006530.

%Y Cf. A035095, A035096.

%K nonn

%O 3,1

%A _Labos Elemer_, Feb 21 2002