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%I #14 Feb 14 2020 03:21:44
%S 1,5,12,50,60,84,300,420,450,756,900,1950,3780,7800,9900,33150,49140,
%T 54600,100800,132600,265200,491400,928200,1856400,8353800,8884200,
%U 16707600,52211250,65995776,78566400,182739375,183783600,208845000,280348992,293046000,329978880
%N Numbers k that are unitary harmonic in Gaussian integers: k * A332476(k) is divisible by A332472(k) + i*A332473(k) (where i is the imaginary unit).
%C Analogous to unitary harmonic numbers (A006086), with the number and sum of unitary divisors functions generalized for Gaussian integers (A332476, A332472 + i * A332473) instead of the number and sum of unitary divisors functions (A034444, A034448).
%H Amiram Eldar, <a href="/A332477/b332477.txt">Table of n, a(n) for n = 1..75</a>
%e 5 is a term since 5 * A332476(5)/(A332472(5) + i*A332473(5)) = 5 * 4/(4 + 8*i) = 1 - 2*i is a Gaussian integer.
%t sigma[p_, e_] := If[Abs[p] == 1, 1, (p^e + 1)]; tau[p_, e_] := If[Abs[p] == 1, 1, 2]; unitaryHarmoincQ[n_] := Divisible[n * Times @@ tau @@@ (f = FactorInteger[n, GaussianIntegers -> True]), Times @@ sigma @@@ f]; Select[Range[10^6], unitaryHarmoincQ]
%Y Cf. A034444, A034448, A006086, A332317, A332472, A332473, A332476.
%K nonn
%O 1,2
%A _Amiram Eldar_, Feb 13 2020
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