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Numbers k such that phi(k) is a perfect 9th power.
8

%I #13 Apr 24 2020 11:01:59

%S 1,2,771,1024,1028,1088,1280,1360,1536,1542,1632,1920,2040,327685,

%T 524288,524296,526336,557056,559232,655360,655370,657920,696320,

%U 699040,786432,786444,789504,835584,838848,983040,986880,1044480,1048560

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

%H Amiram Eldar, <a href="/A078169/b078169.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

%o (PARI) is(n)=ispower(eulerphi(n),9) \\ _Charles R Greathouse IV_, Apr 24 2020

%Y 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.

%K nonn

%O 1,2

%A _Labos Elemer_, Nov 27 2002