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A291959 Numbers n such that the arithmetic, geometric and harmonic means of phi(n) and psi(n) are all integers, where phi(n) is the Euler totient function (A000010) and psi(n) is the Dedekind psi function (A001615).

%I A291959 #9 Oct 06 2019 10:58:32
%S A291959 1,150,300,418,450,525,600,750,836,900,1200,1350,1500,1575,1672,1800,
%T A291959 2250,2400,2625,2700,3000,3135,3344,3600,3675,3750,4050,4500,4598,
%U A291959 4725,4800,5400,6000,6688,6750,7200,7500,7875,7942,8100,9000,9196,9405,9600,10800
%N A291959 Numbers n such that the arithmetic, geometric and harmonic means of phi(n) and psi(n) are all integers, where phi(n) is the Euler totient function (A000010) and psi(n) is the Dedekind psi function (A001615).
%C A291959 The number of terms below 10^3, 10^4, ... are 10, 44, 147, 397, ...
%H A291959 Amiram Eldar, <a href="/A291959/b291959.txt">Table of n, a(n) for n = 1..10000</a>
%e A291959 phi(150)=40, psi(150)=360, their arithmetic mean = 200, geometric mean = 120, harmonic mean = 72 are all integers.
%t A291959 dedekindPsi[n_] := If[n < 1, 0, n Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]];
%t A291959 aQ[n_] := Module[{s = dedekindPsi[n], p = EulerPhi[n]}, IntegerQ[(s + p)/2] && IntegerQ[Sqrt[s*p]] && IntegerQ[2 s*p/(s + p)]]; Select[Range[10^5], aQ]
%Y A291959 Cf. A000010, A001615, A065146.
%K A291959 nonn
%O A291959 1,2
%A A291959 _Amiram Eldar_, Sep 06 2017