A078168 - OEIS

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

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OFFSET

1,2

LINKS

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

EXAMPLE

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.

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 *)

PROG

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

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.

Sequence in context: A190539 A325051 A240551 * A003380 A259310 A060890

Adjacent sequences: A078165 A078166 A078167 * A078169 A078170 A078171

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 27 2002

STATUS

approved