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

1,2

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

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

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.

Sequence in context: A293707 A157315 A244947 * A101578 A041881 A378031

Adjacent sequences: A078163 A078164 A078165 * A078167 A078168 A078169

Keyword

nonn

Author

Labos Elemer, Nov 27 2002

Status

approved