%I
%S 1,1,4,3,4,4,8,1,10,12,12,12,6,8,16,17,6,10,20,12,32,12,24,4,24,
%T 30,28,24,8,48,32,1,48,38,32,30,8,20,24,68,10,32,44,36,40,24,48,
%U 68,50,40,24,18,10,28,48,8,80,64,60,48,12,32,80,63,120
%N The real part of the sum of unitary divisors function (usigma) generalized for Gaussian integers.
%C If n = u * Product_{i} p_i^e_i, where u is a unit (1, i, 1 or i), and p_i is a Gaussian prime with Re(p_i) > 0, then usigma(n) = Product_{i} (p_i^e_i + 1).
%C a(n) = A103228(n) for odd squarefree numbers (A056911), i.e., numbers n such that A318608(n) != 0.
%H Amiram Eldar, <a href="/A332472/b332472.txt">Table of n, a(n) for n = 1..10000</a>
%e a(4) = 3 since 4 = (1 + i)^4 in Gaussian integers (i is the imaginary unit), so usigma(4) = (1 + i)^4 + 1 = 3, and a(4) = Re(3) = 3.
%t f[p_, e_] := If[Abs[p] == 1, 1, (p^e + 1)]; usigma[n_] := Times @@ f @@@ FactorInteger[n, GaussianIntegers > True]; a[n_] := Re[usigma[n]]; Array[a, 100]
%Y Cf. A034448, A103228, A332473 (the imaginary part), A332474 (the norm).
%K sign
%O 1,3
%A _Amiram Eldar_, Feb 13 2020
