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

3,1

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.

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(Magma) [Maximum(PrimeDivisors(EulerPhi(n))): n in [3..90]]; // Vincenzo Librandi, Jan 04 2017
(PARI) a(n) = vecmax(factor(eulerphi(n))[, 1]); \\ Michel Marcus, Jan 04 2017

Crossrefs

Cf. A000010, A006530.

Cf. A035095, A035096.

Sequence in context: A322868 A240975 A242166 * A236832 A089050 A167439

Adjacent sequences: A068208 A068209 A068210 * A068212 A068213 A068214

Keyword

nonn

Author

Labos Elemer, Feb 21 2002

Status

approved