cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A332473 The imaginary part of the sum of unitary divisors function (usigma) generalized for Gaussian integers.

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%I A332473 #10 Feb 14 2020 03:21:56
%S A332473 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 A332473 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 A332473 62,56,96,-64,0,52,0,-96,72,64,0,0,120,96,0,-66,0,128,0
%N A332473 The imaginary part of the sum of unitary divisors function (usigma) generalized for Gaussian integers.
%C A332473 See A332472 for a description.
%H A332473 Amiram Eldar, <a href="/A332473/b332473.txt">Table of n, a(n) for n = 1..10000</a>
%e A332473 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 A332473 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 A332473 Cf. A034448, A103229, A332472 (the real part), A332474 (the norm).
%K A332473 sign
%O A332473 1,2
%A A332473 _Amiram Eldar_, Feb 13 2020