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A068211
Largest prime factor of Euler totient function phi(n).
10
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.
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 21 2002
STATUS
approved