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

Author

Stefan Steinerberger, Feb 17 2006

Keywords

• nonn

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?

Examples

			phi(4096) = 2048 = 2^11.
		

Links

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

Crossrefs

Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power), A000010.

Programs

Mathematica

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

Extensions

More terms from Stefan Steinerberger, May 16 2007