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A078167
Numbers k such that phi(k) is a perfect 7th power.
8
1, 2, 255, 256, 272, 320, 340, 384, 408, 480, 510, 21845, 32768, 32896, 34816, 34952, 40960, 41120, 43520, 43690, 49152, 49344, 52224, 52428, 61440, 61680, 65280, 280999, 281587, 282637, 282949, 283897, 294409, 297449, 300409, 302039, 304399
OFFSET
1,2
LINKS
EXAMPLE
phi of the sequence includes 1, 128, 16384, 279936, etc..; powers arise several times; a(3) = A053576(7) = 255; in sequence rather large jumps arise when power of new numbers appear.
MATHEMATICA
k=7; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 1000000}]
PROG
(PARI) is(n)=ispower(eulerphi(n), 7) \\ Charles R Greathouse IV, Apr 24 2020
CROSSREFS
Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th, this sequence), A078168 (8th), A078169 (9th), A078170 (10th power), A001317, A053576, A045544, A000010.
Sequence in context: A370367 A070782 A370965 * A004875 A067480 A062077
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 27 2002
STATUS
approved