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A078168 Numbers k such that phi(k) is a perfect 8th power. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 27 2002
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)