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A116041
Integers k such that k + phi(k) + phi(phi(k)) is a fourth power.
4
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
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
KEYWORD
nonn
AUTHOR
Giovanni Resta, Feb 13 2006
EXTENSIONS
a(34)-a(36) from Hiroaki Yamanouchi, Sep 19 2014
STATUS
approved