A332476 The number of unitary divisors of n in Gaussian integers.

1, 2, 2, 2, 4, 4, 2, 2, 2, 8, 2, 4, 4, 4, 8, 2, 4, 4, 2, 8, 4, 4, 2, 4, 4, 8, 2, 4, 4, 16, 2, 2, 4, 8, 8, 4, 4, 4, 8, 8, 4, 8, 2, 4, 8, 4, 2, 4, 2, 8, 8, 8, 4, 4, 8, 4, 4, 8, 2, 16, 4, 4, 4, 2, 16, 8, 2, 8, 4, 16, 2, 4, 4, 8, 8, 4, 4, 16, 2, 8, 2, 8, 2, 8, 16

Offset: 1

Author

Amiram Eldar, Feb 13 2020

Keywords

• nonn
• mult

Examples

			a(2) = 2 since 2 = -i * (1 + i)^2, so it has 2 unitary divisors (up to associates): 1 and (1 + i)^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034444, A062327, A086275, A332472, A332473, A332474.

Programs

Mathematica

f[p_, e_] := If[Abs[p] == 1, 1, 2]; a[n_] := Times @@ f @@@ FactorInteger[n, GaussianIntegers -> True]; Array[a, 100]

Formula

Multiplicative with a(p^e) = 4 if p == 1 (mod 4) and 2 otherwise.

a(n) = 2^A086275(n).