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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). 1
 1, 150, 300, 418, 450, 525, 600, 750, 836, 900, 1200, 1350, 1500, 1575, 1672, 1800, 2250, 2400, 2625, 2700, 3000, 3135, 3344, 3600, 3675, 3750, 4050, 4500, 4598, 4725, 4800, 5400, 6000, 6688, 6750, 7200, 7500, 7875, 7942, 8100, 9000, 9196, 9405, 9600, 10800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The number of terms below 10^3, 10^4, ... are 10, 44, 147, 397, ... LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE phi(150)=40, psi(150)=360, their arithmetic mean = 200, geometric mean = 120, harmonic mean = 72 are all integers. MATHEMATICA dedekindPsi[n_] := If[n < 1, 0, n Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]]; 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] CROSSREFS Cf. A000010, A001615, A065146. Sequence in context: A292705 A335145 A063829 * A210643 A211550 A212465 Adjacent sequences:  A291956 A291957 A291958 * A291960 A291961 A291962 KEYWORD nonn AUTHOR Amiram Eldar, Sep 06 2017 STATUS approved

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Last modified September 25 11:39 EDT 2021. Contains 347654 sequences. (Running on oeis4.)