%I #25 Sep 24 2022 00:50:55
%S 1,2,85,128,136,160,170,192,204,240,4369,8192,8224,8704,8738,10240,
%T 10280,10880,12288,12336,13056,15360,15420,16320,47197,47239,47989,
%U 49267,49589,50557,51319,52429,52649,55699,57589,57953,59495,63973
%N Numbers k such that phi(k) is a perfect sixth power.
%C As phi(2^(6*n+1)) = (2^n)^6, A277757 is a subsequence. - _Bernard Schott_, Sep 23 2022
%H Amiram Eldar, <a href="/A078166/b078166.txt">Table of n, a(n) for n = 1..10000</a>
%e phi of the sequence includes 1, 64, 4096, 46656,..; powers arise several times; a(3)= A053576(6) = 85; in sequence relatively large jumps are observable when power of new numbers appear.
%t k=6; Select[Range[65000],IntegerQ[EulerPhi[#]^(1/k)]&] (* _Harvey P. Dale_, Feb 20 2011 *)
%o (PARI) is(n)=ispower(eulerphi(n),6) \\ _Charles R Greathouse IV_, Apr 24 2020
%Y A277757 is a subsequence.
%Y Numbers k such that phi(k) is a perfect power: A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th, this sequence), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power).
%Y Cf. A001317, A053576, A045544, A000010.
%K nonn
%O 1,2
%A _Labos Elemer_, Nov 27 2002
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