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A332008
Numbers k such that phi(k) and phi(k+1) are perfect powers (A001597).
0
1, 15, 16, 63, 101, 125, 255, 256, 272, 504, 512, 513, 629, 679, 1358, 1359, 1728, 1970, 2047, 2222, 2509, 2834, 3458, 3705, 4094, 4095, 4400, 4577, 4616, 4913, 5403, 6817, 7295, 7956, 8729, 11667, 11672, 16132, 16384, 16523, 17507, 23085, 24198, 24564, 24624, 25220, 25601, 27216, 27384, 28564, 29444
OFFSET
1,2
EXAMPLE
phi(101) = 10^2, and phi(102) = 2^5.
phi(3458) = 6^4, and phi(3459) = 48^2.
MATHEMATICA
perfectPowerQ[1] = True; perfectPowerQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[30000], And @@ perfectPowerQ /@ EulerPhi[# + {0, 1}] &] (* Amiram Eldar, Feb 04 2020 *)
PROG
(PARI) v=[1]; for(i = 2, 30000, if(ispower(eulerphi(i)), if(ispower(eulerphi(i+1)), v = concat(v, i)))); v
(Magma) [1] cat [k:k in [3..30000]|IsPower(EulerPhi(k)) and IsPower(EulerPhi(k+1))]; // Marius A. Burtea, Feb 05 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Antonio Roldán, Feb 04 2020
STATUS
approved