|
%I #15 Sep 13 2020 11:27:31
%S 1,3,15,19,95,104,125,164,194,255,259,341,491,495,504,512,513,584,591,
%T 629,679,755,775,975,1024,1147,1247,1254,1260,1313,1358,1463,1469,
%U 1538,1615,1728,1919,1962,1970,2047,2071,2090,2204,2299,2321,2345,2404,2625
%N Numbers k such that the geometric mean of the Euler totient function of k and k+1 is an integer.
%H Amiram Eldar, <a href="/A083545/b083545.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = x is such that sqrt(A000010(x)*A000010(x+1)) is an integer. Values of solutions x to phi(x) * phi(x+1) = A083542(x) = y^2.
%e 19 is a term since phi(19) = 18, phi(20) = 8, 8*18 = 144 = 12^2.
%t f[x_] := EulerPhi[x]; Do[s=Sqrt[f[n+1]*f[n]]; If[IntegerQ[s], Print[n]], {n, 1, 5000}]
%t Position[Partition[EulerPhi[Range[2700]],2,1],_?(IntegerQ[GeometricMean[ #]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Sep 13 2020 *)
%Y Cf. A000010, A083542, A066813, A058515, A083538, A083542, A083546.
%K nonn
%O 1,2
%A _Labos Elemer_, May 21 2003
|
