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 A332474 The norm of the sum of unitary divisors function (usigma) generalized for Gaussian integers. 6
 1, 5, 16, 9, 80, 80, 64, 65, 100, 400, 144, 144, 360, 320, 1280, 289, 520, 500, 400, 720, 1024, 720, 576, 1040, 640, 1800, 784, 576, 1360, 6400, 1024, 1025, 2304, 2600, 5120, 900, 2000, 2000, 5760, 5200, 2600, 5120, 1936, 1296, 8000, 2880, 2304, 4624, 2500, 3200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A332472 for a description. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A332472(n)^2 + A332473(n)^2. EXAMPLE 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. MATHEMATICA 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] CROSSREFS Cf. A034448, A103230, A332472 (the real part), A332473 (the imaginary part). Sequence in context: A063927 A195869 A101752 * A195866 A075805 A095872 Adjacent sequences:  A332471 A332472 A332473 * A332475 A332476 A332477 KEYWORD nonn AUTHOR Amiram Eldar, Feb 13 2020 STATUS approved

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Last modified August 17 23:13 EDT 2022. Contains 356204 sequences. (Running on oeis4.)