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

1,2

Links

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

Formula

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A071472 A367120 A064135 * A179651 A139560 A192095

Adjacent sequences: A332473 A332474 A332475 * A332477 A332478 A332479

Keyword

nonn,mult

Author

Amiram Eldar, Feb 13 2020

Status

approved