A078169 Numbers k such that phi(k) is a perfect 9th power.

1, 2, 771, 1024, 1028, 1088, 1280, 1360, 1536, 1542, 1632, 1920, 2040, 327685, 524288, 524296, 526336, 557056, 559232, 655360, 655370, 657920, 696320, 699040, 786432, 786444, 789504, 835584, 838848, 983040, 986880, 1044480, 1048560

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

phi of the sequence includes 1, 512, 262144,.. etc.; powers arise several times; a(3) = A053576(9) = 771; in sequence smoother ranges and quite large jumps arise when power of new numbers appear as phi-values.

Mathematica

k=9; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 10000000}]

Prog

(PARI) is(n)=ispower(eulerphi(n), 9) \\ Charles R Greathouse IV, Apr 24 2020

Crossrefs

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

Sequence in context: A344663 A167448 A320481 * A226779 A375844 A243409

Adjacent sequences: A078166 A078167 A078168 * A078170 A078171 A078172

Keyword

nonn

Author

Labos Elemer, Nov 27 2002

Status

approved