login
n*phi(n)*phi(phi(n)) is a square.
3

%I #5 Nov 21 2013 12:48:48

%S 1,8,27,32,108,128,243,250,432,512,686,972,1000,1331,1728,2048,2187,

%T 2197,2744,3375,3888,4000,5324,6174,6250,6912,8192,8748,8788,9826,

%U 10976,13500,15552,16000,19683,19773,21296,24696,25000,27648,30375

%N n*phi(n)*phi(phi(n)) is a square.

%H Harvey P. Dale, <a href="/A116002/b116002.txt">Table of n, a(n) for n = 1..220</a>

%e 15552*phi(15552)*phi(phi(15552))=373248^2.

%t esQ[n_]:=Module[{e=EulerPhi[n]},IntegerQ[Sqrt[n e EulerPhi[e]]]]; Select[Range[31000],esQ] (* _Harvey P. Dale_, Dec 16 2011 *)

%Y Cf. A055744.

%K nonn

%O 1,2

%A _Giovanni Resta_, Feb 13 2006