A114573 Numbers k such that phi(k) is a perfect 11th power.

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

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: A094211 A372116 A350418 * A285086 A367436 A024035

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