A103230 Norm of the sum of divisors function sigma(n) generalized for Gaussian integers.

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

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