A065528 Numbers n such that phi(n) is a nontrivial power b^c where b > 1 and c > 1.

5, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 37, 40, 48, 51, 57, 60, 63, 64, 68, 74, 76, 80, 85, 96, 101, 102, 108, 114, 120, 125, 126, 128, 136, 160, 170, 185, 192, 197, 202, 204, 219, 240, 247, 250, 255, 256, 257, 259, 272, 273, 285, 292, 296, 304, 315, 320, 327, 333

Offset: 1

Author

Joseph L. Pe, Nov 27 2001

Keywords

• nonn
• easy

Comments

What values of b can occur?

Apparently all even numbers can occur as values of b. Checked up to 50000; see A227533. - Charles R Greathouse IV, Jul 15 2013

Examples

			phi(63) = 6^2, phi(96) = 2^5.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A166955.

Programs

Mathematica

ppQ[n_] := GCD @@ Last /@ FactorInteger@ n > 1; Select[ Range@ 330, ppQ@ EulerPhi@ # &] (* Robert G. Wilson v, Jul 16 2013 *)

PARI

v=[]; for(n=2, 333, if(ispower(eulerphi(n)), v=concat(v, n))); v (Hobson)

PARI

is(n)=ispower(eulerphi(n)) \\ Charles R Greathouse IV, Jul 15 2013

Formula

a(n) = A166955(n+2). - Juri-Stepan Gerasimov, Oct 25 2009

Extensions

More terms from Nick Hobson, Nov 29 2006

b-file from Charles R Greathouse IV, Mar 25 2010