A227533 - OEIS

%I #12 Jul 19 2013 09:12:54

%S 2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,4,2,3,2,2,2,4,2,2,2,2,2,3,2,5,2,2,2,

%T 2,2,2,3,3,2,4,2,15,2,2,4,2,2,3,2,3,2,4,2,2,2,2,2,3,2,7,2,2,2,2,2,2,2,

%U 4,2,3,2,2,2,2,3,3,2,8,2,2,4,15,2,2,3,2,2,5,2,4,2,2

%N Smallest e > 1 such that (2n)^e is a totient, or 0 if no such e exists.

%C Conjecture: a(n) > 0 for all n.

%H Charles R Greathouse IV, <a href="/A227533/b227533.txt">Table of n, a(n) for n = 1..100000</a>

%H Charles R Greathouse IV, <a href="/A227533/a227533.gp.txt">GP script for efficiently computing the sequence</a>

%e a(1) = 2 because phi(5) = 2^2. a(11) = 3 because phi(13315) = 22^3 but phi(k) is not equal to 22^2 for any k.

%o (PARI) a(n)=my(k=2);while(!istotient((2*n)^k),k++);k

%Y Cf. A000010, A002202, A065528, A227534, A227535.

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Jul 14 2013