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A078168
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Numbers k such that phi(k) is a perfect 8th power.
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8
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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
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1,2
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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