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%I #7 Apr 19 2022 07:26:37
%S 90,40682250,81364500,105773850,423095400,1798155450,14385243600
%N Unitary harmonic numbers (A006086) that are not unitary arithmetic numbers (A103826).
%C There are 290 unitary harmonic numbers below 10^12, and only 7 of them are in this sequence.
%e 90 is in the sequence since its unitary divisors are {1, 2, 5, 9, 10, 18, 45, 90}, their harmonic mean, 4, is an integer, but their arithmetic mean, 45/2, is not.
%t q[n_] := Module[{f = FactorInteger[n], d, s}, d = 2^Length[f]; s = Times @@ (1 + Power @@@ f); IntegerQ[n*d/s] && !IntegerQ[s/d]]; Select[Range[5*10^7], q]
%Y The unitary version of A046999.
%Y Subsequence of A006086.
%Y Cf. A006087, A103826.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Apr 19 2022