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Unitary arithmetic numbers k whose mean unitary divisor is a unitary divisor of k.
3

%I #12 Mar 05 2023 05:21:23

%S 1,6,60,420,630,5460,8190,16632,64260,143640,172900,598500,716625,

%T 790398,791700,1182384,1187550,1530144,2708160,4277448,5314680,

%U 6284250,6397300,6741630,14619150,15214500,22144500,24315984,87966648,93284100,161670600,165197760,232517250

%N Unitary arithmetic numbers k whose mean unitary divisor is a unitary divisor of k.

%C Also, unitary harmonic numbers k whose harmonic mean of the unitary divisors of k is a unitary divisor of k.

%H Amiram Eldar, <a href="/A353039/b353039.txt">Table of n, a(n) for n = 1..84</a>

%e 6 is a term since the arithmetic mean of its unitary divisors, {1, 2, 3, 6}, is 3, and 3 is also a unitary divisor of 6.

%t q[n_] := Module[{f = FactorInteger[n], d, s, m}, d = 2^Length[f]; s = Times @@ (1 + Power @@@ f); m = s/d; IntegerQ[m] && Divisible[n, m] && CoprimeQ[m, n/m]]; Select[Range[10^6], q]

%Y Subsequence of A006086 and A103826.

%Y Cf. A007340.

%K nonn

%O 1,2

%A _Amiram Eldar_, Apr 19 2022