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%I #9 Mar 06 2020 00:57:52
%S 1,2,3855,4096,4112,4352,5120,5140,5440,6144,6168,6528,7680,7710,8160,
%T 5570645,8388608,8388736,8421376,8912896,8913032,8947712,10485760,
%U 10485920,10526720,11141120,11141290,11184640,12582912,12583104
%N Numbers k such that phi(k) is a perfect 11th power.
%C Given the fact that phi(n) > sqrt(n) for all n except n=2 and n=6 we can see that every 11th power does appear as value only a finite number of times. What bounds on the density of this sequence can be proved?
%H Amiram Eldar, <a href="/A114573/b114573.txt">Table of n, a(n) for n = 1..3625</a>
%e phi(4096) = 2048 = 2^11.
%t For[n = 1, n < 100000, n++, If[EulerPhi[n]^(1/11) == Floor[EulerPhi[n]^(1/11)], Print[n]]]
%Y Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power), A000010.
%K nonn
%O 1,2
%A _Stefan Steinerberger_, Feb 17 2006
%E More terms from _Stefan Steinerberger_, May 16 2007
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