This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A114573 #9 Mar 06 2020 00:57:52 %S A114573 1,2,3855,4096,4112,4352,5120,5140,5440,6144,6168,6528,7680,7710,8160, %T A114573 5570645,8388608,8388736,8421376,8912896,8913032,8947712,10485760, %U A114573 10485920,10526720,11141120,11141290,11184640,12582912,12583104 %N A114573 Numbers k such that phi(k) is a perfect 11th power. %C A114573 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 A114573 Amiram Eldar, <a href="/A114573/b114573.txt">Table of n, a(n) for n = 1..3625</a> %e A114573 phi(4096) = 2048 = 2^11. %t A114573 For[n = 1, n < 100000, n++, If[EulerPhi[n]^(1/11) == Floor[EulerPhi[n]^(1/11)], Print[n]]] %Y A114573 Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power), A000010. %K A114573 nonn %O A114573 1,2 %A A114573 _Stefan Steinerberger_, Feb 17 2006 %E A114573 More terms from _Stefan Steinerberger_, May 16 2007