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 A078165 #25 Sep 27 2022 04:03:43
%S A078165 1,2,51,64,68,80,96,102,120,1285,2048,2056,2176,2560,2570,2720,3072,
%T A078165 3084,3264,3840,4080,7957,8227,8279,9079,9139,9709,9919,10355,10595,
%U A078165 11667,11673,11691,12099,12393,12483,12753,12987,13797,14715,14763
%N A078165 Numbers k such that phi(k) is a perfect 5th power.
%C A078165 As phi(2^(5*n+1)) = (2^n)^5, A013822 is a subsequence. - _Bernard Schott_, Sep 26 2022
%C A078165 Numbers of the form u = 2^(5*k)*3^(5*m + 1), k>=1, m>=0, are terms because phi(u) = 2^(5*k)*3^(5*m) = (2^k*3^m)^5. - _Marius A. Burtea_, Sep 26 2022
%H A078165 Amiram Eldar, <a href="/A078165/b078165.txt">Table of n, a(n) for n = 1..10000</a>
%e A078165 phi of the sequence includes 1, 32, 1024, 7776, ...; powers arise several times; a(3) = A053576(5) = 51.
%t A078165 k=5; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 5000}]
%t A078165 Select[Range[15000],IntegerQ[Surd[EulerPhi[#],5]]&] (* _Harvey P. Dale_, Jul 26 2019 *)
%o A078165 (PARI) is(n)=ispower(eulerphi(n),5) \\ _Charles R Greathouse IV_, Apr 24 2020
%Y A078165 A013822 is a subsequence.
%Y A078165 Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th, this sequence), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power), A001317, A053576, A045544, A000010.
%K A078165 nonn
%O A078165 1,2
%A A078165 _Labos Elemer_, Nov 27 2002