A116041 - OEIS

%I #19 Sep 11 2024 10:08:23

%S 10,160,301,752,912,1033,2560,2801,6277,11852,12032,12661,14592,27297,

%T 35809,38576,40960,73872,96688,123601,133904,151312,183589,189632,

%U 192512,233472,561168,578448,617216,629212,655360,714133,722701,1181952,1263681,1264481

%N Integers k such that k + phi(k) + phi(phi(k)) is a fourth power.

%H Hiroaki Yamanouchi, <a href="/A116041/b116041.txt">Table of n, a(n) for n = 1..272</a>

%e 6277+phi(6277)+phi(phi(6277)) = 14641 = 11^4, so 6277 is a term.

%t fpQ[n_]:=Module[{epn=EulerPhi[n]},IntegerQ[Power[n+epn+ EulerPhi[epn], (4)^-1]]]; Select[Range[800000],fpQ] (* _Harvey P. Dale_, Mar 23 2011 *)

%o (PARI)

%o for(n=1,10^7,p = n+eulerphi(n)+eulerphi(eulerphi(n)); if(ispower(p)&&ispower(p)%4==0, print1(n,", "))) \\ _Derek Orr_, Sep 19 2014

%Y Cf. A116040, A116042, A116043.

%K nonn

%O 1,1

%A _Giovanni Resta_, Feb 13 2006

%E a(34)-a(36) from _Hiroaki Yamanouchi_, Sep 19 2014