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%I #8 Oct 30 2021 08:22:54
%S 321048,448335,1284192,1605240,1672125,1862190,3531528,5016375,
%T 5457816,6420960,7384104,7621695,8026200,9310392,9952488,10311705,
%U 11878776,13001715,13035330,13162968,13805064,13898385,14126112,15089256,16588395,17015544,17657640,17836000
%N Numbers m such that there is at least two smaller numbers k < m with the same harmonic mean of divisors as m.
%C What is the least term m with more than two smaller numbers k with the same harmonic mean of divisors as m?
%e 321048 is a term since the harmonic mean of divisors of 321048 is 3528/125, and it is also the harmonic mean of divisors of both 201096 and 296352 which are smaller than 321048.
%t h = Table[DivisorSigma[0, n]/DivisorSigma[-1, n], {n, 1, 2*10^6}]; i = Position[(t = Tally[h])[[;; , 2]], _?(# > 2 &)] // Flatten; Position[h, #][[3 ;; -1]] & /@ t[[i, 1]] // Flatten // Sort
%Y Cf. A099377, A099378, A348696.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 30 2021