A078165 Numbers k such that phi(k) is a perfect 5th power.

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

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

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

Adjacent sequences: A078162 A078163 A078164 * A078166 A078167 A078168

Keyword

nonn

Author

Labos Elemer, Nov 27 2002

Status

approved