

A114573


Numbers k such that phi(k) is a perfect 11th power.


1



1, 2, 3855, 4096, 4112, 4352, 5120, 5140, 5440, 6144, 6168, 6528, 7680, 7710, 8160, 5570645, 8388608, 8388736, 8421376, 8912896, 8913032, 8947712, 10485760, 10485920, 10526720, 11141120, 11141290, 11184640, 12582912, 12583104
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OFFSET

1,2


COMMENTS

Given the fact that phi(n) > sqrt(n) for all n except n=2 and n=6 we can see that every 11th power does appear as value only a finite number of times. What bounds on the density of this sequence can be proved?


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..3625


EXAMPLE

phi(4096) = 2048 = 2^11.


MATHEMATICA

For[n = 1, n < 100000, n++, If[EulerPhi[n]^(1/11) == Floor[EulerPhi[n]^(1/11)], Print[n]]]


CROSSREFS

Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power), A000010.
Sequence in context: A065671 A094211 A350418 * A285086 A024035 A048831
Adjacent sequences: A114570 A114571 A114572 * A114574 A114575 A114576


KEYWORD

nonn


AUTHOR

Stefan Steinerberger, Feb 17 2006


EXTENSIONS

More terms from Stefan Steinerberger, May 16 2007


STATUS

approved



