A332008 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..51.

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 *)

perfPQ[n_]:=GCD@@FactorInteger[n][[;; , 2]]>1; Join[{1}, SequencePosition[Table[If[perfPQ[EulerPhi[n]], 1, 0], {n, 30000}], {1, 1}][[;; , 1]]] (* Harvey P. Dale, Oct 16 2025 *)

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

Cf. A000010, A001597, A166955, A281016.

Sequence in context: A041464 A041460 A041466 * A152044 A041468 A041470

Adjacent sequences: A332005 A332006 A332007 * A332009 A332010 A332011

KEYWORD

nonn

AUTHOR

Antonio Roldán, Feb 04 2020

STATUS

approved