A332008 Numbers k such that phi(k) and phi(k+1) are perfect powers (A001597).
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
Keywords
Examples
phi(101) = 10^2, and phi(102) = 2^5. phi(3458) = 6^4, and phi(3459) = 48^2.
Programs
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Magma
[1] cat [k:k in [3..30000]|IsPower(EulerPhi(k)) and IsPower(EulerPhi(k+1))]; // Marius A. Burtea, Feb 05 2020
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Mathematica
perfectPowerQ[1] = True; perfectPowerQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[30000], And @@ perfectPowerQ /@ EulerPhi[# + {0, 1}] &] (* Amiram Eldar, Feb 04 2020 *) -
PARI
v=[1]; for(i = 2, 30000, if(ispower(eulerphi(i)), if(ispower(eulerphi(i+1)), v = concat(v, i)))); v