A239627 Factored over the Gaussian integers, n has a(n) distinct prime factors, including units -1, i, and -i.

1, 2, 1, 2, 3, 3, 1, 2, 1, 4, 1, 3, 3, 3, 4, 1, 3, 3, 1, 4, 2, 3, 1, 3, 3, 4, 1, 3, 3, 5, 1, 2, 2, 4, 4, 3, 3, 3, 4, 3, 3, 4, 1, 3, 4, 3, 1, 2, 1, 4, 4, 4, 3, 3, 4, 3, 2, 4, 1, 5, 3, 3, 2, 2, 5, 4, 1, 4, 2, 5, 1, 3, 3, 4, 4, 3, 2, 5, 1, 4, 1, 4, 1, 4, 5, 3, 4

Offset: 1

Author

T. D. Noe, Mar 31 2014

Keywords

• nonn

Comments

Here -1, i, and -i are counted as factors. The factor 1 is counted only in a(1).

Examples

			a(2) = 2 because 2 = -i * (1 + i)^2.
a(3) = 1 because 3 is prime over the complex numbers.
a(4) = 2 because 4 = -1 * (1 + i)^4.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A001222 (integer factorizations).

Cf. A078458, A086275 (Gaussian factorizations).

Cf. A239626 (Gaussian factorization including units).

Programs

Mathematica

Table[Length[FactorInteger[n, GaussianIntegers -> True]], {n, 100}]