A078166 Numbers k such that phi(k) is a perfect sixth power.

1, 2, 85, 128, 136, 160, 170, 192, 204, 240, 4369, 8192, 8224, 8704, 8738, 10240, 10280, 10880, 12288, 12336, 13056, 15360, 15420, 16320, 47197, 47239, 47989, 49267, 49589, 50557, 51319, 52429, 52649, 55699, 57589, 57953, 59495, 63973

Offset: 1

Author

Labos Elemer, Nov 27 2002

Keywords

• nonn

Comments

As phi(2^(6*n+1)) = (2^n)^6, A277757 is a subsequence. - Bernard Schott, Sep 23 2022

Examples

			phi of the sequence includes 1, 64, 4096, 46656,..; powers arise several times; a(3)= A053576(6) = 85; in sequence relatively large jumps are observable when power of new numbers appear.
		

Links

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

Crossrefs

A277757 is a subsequence.

Numbers k such that phi(k) is a perfect power: A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th, this sequence), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power).

Cf. A001317, A053576, A045544, A000010.

Programs

Mathematica

k=6; Select[Range[65000],IntegerQ[EulerPhi[#]^(1/k)]&]  (* Harvey P. Dale, Feb 20 2011 *)

PARI

is(n)=ispower(eulerphi(n),6) \\ Charles R Greathouse IV, Apr 24 2020