A259788 - OEIS

%I #21 Jul 19 2015 08:56:15

%S 2,2,3,3,5,5,5,5,5,3,11,11,11,11,11,11,11,11,11,11,11,7,23,23,23,23,

%T 23,23,29,29,29,29,29,29,29,29,29,29,29,29,41,41,41,41,41,41,41,41,41,

%U 41,41,41,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,53,83,83,83,83,83,83,89

%N Greatest prime factor of phi(binomial(2*n,n)).

%C Conjectures:

%C (1) 7 is a unique term which is not a Sophie Germain prime (A005384);

%C (2) A Sophie Germain prime p occurs p times if and only if p=2,3,5 and 11; otherwise, it occurs q-p times, where q is the next Sophie Germain prime > p;

%C (3) a(n) is the greatest prime factor of p-1 for primes p in the interval (n, 2*n).

%C All these conjectures follow from the following strengthening of the Bertrand postulate for n>=24: the interval (n, 2*n) contains a safe prime (A005385).

%H Peter J. C. Moses, <a href="/A259788/b259788.txt">Table of n, a(n) for n = 2..5001</a>

%t Map[First[Last[FactorInteger[EulerPhi[Binomial[2#,#]]]]]&,Range[2,100]]

%Y Cf. A000010, A000984, A005384, A005385, A006530, A066973.

%K nonn

%O 2,1

%A _Vladimir Shevelev_, Jul 05 2015