%I #11 Sep 30 2018 04:31:00
%S 1,270,164989440,2701389600,71271827200,183694492800,7322605472000,
%T 28103080287744
%N Harmonic numbers k such that the harmonic mean of the divisors of k is also a harmonic number.
%C The harmonic means of the divisors of the terms are 1, 6, 140, 270, 270, 672, 672, 496.
%C The terms 1, 2701389600 and 71271827200 have harmonic means of divisors which are also in this sequence.
%e 270 is in the sequence since the harmonic mean of its divisors is 6, which is also a harmonic number.
%t hQ[n_] := IntegerQ[n*DivisorSigma[0, n]/DivisorSigma[1, n]]; hhQ[n_] := Module[{h = n * DivisorSigma[0, n]/DivisorSigma[1, n]}, IntegerQ[h] && hQ[h]]; Do[If[hhQ[n], Print[n]], {n, 1, 10^14}]
%Y Cf. A001599, A317477.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Jul 29 2018