A078168 - OEIS

%I #15 Apr 24 2020 11:01:39

%S 1,2,257,512,514,544,640,680,768,816,960,1020,65537,131072,131074,

%T 131584,139264,139808,163840,164480,174080,174760,196608,197376,

%U 208896,209712,245760,246720,261120,262140,1682227,1683109,1683559,1683937

%N Numbers k such that phi(k) is a perfect 8th power.

%H Amiram Eldar, <a href="/A078168/b078168.txt">Table of n, a(n) for n = 1..7500</a>

%e phi of the sequence includes 1, 256, 65536, 1679616, etc.; powers arise several times; a(3) = A053576(7) = 257; in sequence smoother ranges and quite large jumps arise when power of new numbers appear as phi-values.

%t k=8; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 10000000}]

%t Select[Range[2*10^6],IntegerQ[Surd[EulerPhi[#],8]]&] (* _Harvey P. Dale_, Oct 20 2014 *)

%o (PARI) is(n)=ispower(eulerphi(n),8) \\ _Charles R Greathouse IV_, Apr 24 2020

%Y Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th), A078168 (8th, this sequence), A078169 (9th), A078170 (10th power), A001317, A053576, A045544, A000010.

%K nonn

%O 1,2

%A _Labos Elemer_, Nov 27 2002