A116041 Integers k such that k + phi(k) + phi(phi(k)) is a fourth power.

10, 160, 301, 752, 912, 1033, 2560, 2801, 6277, 11852, 12032, 12661, 14592, 27297, 35809, 38576, 40960, 73872, 96688, 123601, 133904, 151312, 183589, 189632, 192512, 233472, 561168, 578448, 617216, 629212, 655360, 714133, 722701, 1181952, 1263681, 1264481

Offset

1,1

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..272

Example

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

Mathematica

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

Prog

(PARI)
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

Crossrefs

Cf. A116040, A116042, A116043.

Sequence in context: A239762 A087961 A360935 * A284110 A180881 A106261

Adjacent sequences: A116038 A116039 A116040 * A116042 A116043 A116044

Keyword

nonn

Author

Giovanni Resta, Feb 13 2006

Extensions

a(34)-a(36) from Hiroaki Yamanouchi, Sep 19 2014

Status

approved