A078168 Numbers k such that phi(k) is a perfect 8th power.

1, 2, 257, 512, 514, 544, 640, 680, 768, 816, 960, 1020, 65537, 131072, 131074, 131584, 139264, 139808, 163840, 164480, 174080, 174760, 196608, 197376, 208896, 209712, 245760, 246720, 261120, 262140, 1682227, 1683109, 1683559, 1683937

Offset: 1

Author

Labos Elemer, Nov 27 2002

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..7500

Crossrefs

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.

Programs

Mathematica

k=8; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 10000000}]
Select[Range[2*10^6],IntegerQ[Surd[EulerPhi[#],8]]&] (* Harvey P. Dale, Oct 20 2014 *)

PARI

is(n)=ispower(eulerphi(n),8) \\ Charles R Greathouse IV, Apr 24 2020