

A332472


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


6



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, 30, 28, 24, 8, 48, 32, 1, 48, 38, 32, 30, 8, 20, 24, 68, 10, 32, 44, 36, 40, 24, 48, 68, 50, 40, 24, 18, 10, 28, 48, 8, 80, 64, 60, 48, 12, 32, 80, 63, 120
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OFFSET

1,3


COMMENTS

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).


LINKS



EXAMPLE

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.


MATHEMATICA

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]


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



