A332474 The norm of the sum of unitary divisors function (usigma) generalized for Gaussian integers.

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

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 A363342 A075805

Adjacent sequences: A332471 A332472 A332473 * A332475 A332476 A332477

Keyword

nonn

Author

Amiram Eldar, Feb 13 2020

Status

approved