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 A103230 Norm of the sum of divisors function sigma(n) generalized for Gaussian integers. 19
 1, 13, 16, 41, 80, 208, 64, 113, 169, 1040, 144, 656, 360, 832, 1280, 481, 520, 2197, 400, 3280, 1024, 1872, 576, 1808, 2257, 4680, 1600, 2624, 1360, 16640, 1024, 2113, 2304, 6760, 5120, 6929, 2000, 5200, 5760, 9040, 2600, 13312, 1936, 5904, 13520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A102506 for a complete description. See A103228 and A103229 for the real and imaginary parts. Multiplicative because the sigma function on Gaussian integers as defined in A102506 is multiplicative and the norm is completely multiplicative. - Andrew Howroyd, Aug 03 2018 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Andrew Howroyd) FORMULA a(n) = A103228(n)^2 + A103229(n)^2. - Andrew Howroyd, Aug 03 2018 MATHEMATICA Abs[Table[DivisorSigma[1, n, GaussianIntegers -> True], {n, 100}]]^2 PROG (PARI) \\ See A102506 for formula. CSigma(z)={my(f=factor(z, I)); prod(i=1, #f~, my([p, e]=f[i, ]); if(norm(p)==1, 1, (p^(e+1)-1)/(p-1)))} a(n)=norm(CSigma(n)); \\ Andrew Howroyd, Aug 03 2018 CROSSREFS Cf. A102506, A102574, A103224, A103228, A103229. Sequence in context: A352664 A056663 A274978 * A217179 A107081 A029526 Adjacent sequences:  A103227 A103228 A103229 * A103231 A103232 A103233 KEYWORD nonn,mult AUTHOR T. D. Noe, Jan 26 2005 STATUS approved

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Last modified October 3 06:40 EDT 2022. Contains 357231 sequences. (Running on oeis4.)