A068211 Largest prime factor of Euler totient function phi(n).

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, 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, 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

Offset: 3

Author

Labos Elemer, Feb 21 2002

Keywords

• nonn

Comments

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.

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A000010, A006530.

Cf. A035095, A035096.

Programs

Magma

[Maximum(PrimeDivisors(EulerPhi(n))): n in [3..90]]; // Vincenzo Librandi, Jan 04 2017

Mathematica

Table[FactorInteger[EulerPhi[n]][[-1, 1]], {n, 3, 100}] (* Vincenzo Librandi, Jan 04 2017 *)

PARI

a(n) = vecmax(factor(eulerphi(n))[,1]); \\ Michel Marcus, Jan 04 2017

Formula

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