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%I #10 Feb 14 2020 03:22:22
%S 1,5,16,9,80,80,64,65,100,400,144,144,360,320,1280,289,520,500,400,
%T 720,1024,720,576,1040,640,1800,784,576,1360,6400,1024,1025,2304,2600,
%U 5120,900,2000,2000,5760,5200,2600,5120,1936,1296,8000,2880,2304,4624,2500,3200
%N The norm of the sum of unitary divisors function (usigma) generalized for Gaussian integers.
%C See A332472 for a description.
%H Amiram Eldar, <a href="/A332474/b332474.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A332472(n)^2 + A332473(n)^2.
%e a(4) = 9 since 4 = -(1 + i)^4 in Gaussian integers (i is the imaginary unit), so usigma(4) = (1 + i)^4 + 1 = -3, and a(4) = (-3)^2 + 0^2 = 9.
%t f[p_, e_] := If[Abs[p] == 1, 1, (p^e + 1)]; usigma[n_] := Times @@ f @@@ FactorInteger[n, GaussianIntegers -> True]; a[n_] := Abs[usigma[n]]^2; Array[a, 100]
%Y Cf. A034448, A103230, A332472 (the real part), A332473 (the imaginary part).
%K nonn
%O 1,2
%A _Amiram Eldar_, Feb 13 2020
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