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A078165
Numbers k such that phi(k) is a perfect 5th power.
8
1, 2, 51, 64, 68, 80, 96, 102, 120, 1285, 2048, 2056, 2176, 2560, 2570, 2720, 3072, 3084, 3264, 3840, 4080, 7957, 8227, 8279, 9079, 9139, 9709, 9919, 10355, 10595, 11667, 11673, 11691, 12099, 12393, 12483, 12753, 12987, 13797, 14715, 14763
OFFSET
1,2
COMMENTS
As phi(2^(5*n+1)) = (2^n)^5, A013822 is a subsequence. - Bernard Schott, Sep 26 2022
Numbers of the form u = 2^(5*k)*3^(5*m + 1), k>=1, m>=0, are terms because phi(u) = 2^(5*k)*3^(5*m) = (2^k*3^m)^5. - Marius A. Burtea, Sep 26 2022
LINKS
EXAMPLE
phi of the sequence includes 1, 32, 1024, 7776, ...; powers arise several times; a(3) = A053576(5) = 51.
MATHEMATICA
k=5; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 5000}]
Select[Range[15000], IntegerQ[Surd[EulerPhi[#], 5]]&] (* Harvey P. Dale, Jul 26 2019 *)
PROG
(PARI) is(n)=ispower(eulerphi(n), 5) \\ Charles R Greathouse IV, Apr 24 2020
CROSSREFS
A013822 is a subsequence.
Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th, this sequence), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power), A001317, A053576, A045544, A000010.
Sequence in context: A230561 A057943 A037419 * A180110 A037058 A106042
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 27 2002
STATUS
approved