A332473 - OEIS

%I #10 Feb 14 2020 03:21:56

%S 0,2,0,0,8,8,0,-8,0,16,0,0,18,16,32,0,22,20,0,-24,0,24,0,-32,8,30,0,0,

%T 36,64,0,32,0,34,64,0,44,40,72,-24,50,64,0,0,80,48,0,0,0,-40,88,-54,

%U 62,56,96,-64,0,52,0,-96,72,64,0,0,120,96,0,-66,0,128,0

%N The imaginary part of the sum of unitary divisors function (usigma) generalized for Gaussian integers.

%C See A332472 for a description.

%H Amiram Eldar, <a href="/A332473/b332473.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 0 since 4 = -(1 + i)^4 in Gaussian integers (i is the imaginary unit), so usigma(4) = (1 + i)^4 + 1 = -3, and a(4) = Im(-3) = 0.

%t f[p_, e_] := If[Abs[p] == 1, 1, (p^e + 1)]; usigma[n_] := Times @@ f @@@ FactorInteger[n, GaussianIntegers -> True]; a[n_] := Im[usigma[n]]; Array[a, 100]

%Y Cf. A034448, A103229, A332472 (the real part), A332474 (the norm).

%K sign

%O 1,2

%A _Amiram Eldar_, Feb 13 2020