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A078166
Numbers k such that phi(k) is a perfect sixth power.
8
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
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).
Sequence in context: A293707 A157315 A244947 * A101578 A041881 A378031
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 27 2002
STATUS
approved