A239626 Factored over the Gaussian integers, n has a(n) prime factors counted multiply, including units -1, i, and -i.

1, 3, 1, 5, 3, 4, 1, 7, 2, 5, 1, 6, 3, 4, 4, 8, 3, 5, 1, 7, 2, 4, 1, 8, 5, 5, 3, 6, 3, 6, 1, 11, 2, 5, 4, 7, 3, 4, 4, 8, 3, 5, 1, 6, 5, 4, 1, 9, 2, 7, 4, 7, 3, 6, 4, 8, 2, 5, 1, 8, 3, 4, 3, 13, 5, 5, 1, 7, 2, 6, 1, 9, 3, 5, 6, 6, 2, 6, 1, 11, 4, 5, 1, 7, 5, 4, 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) = 3 because 2 = -i * (1 + i)^2.
a(3) = 1 because 3 is prime over the complex numbers.
a(4) = 5 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. A239627 (Gaussian factorization including units).

Programs

Mathematica

Table[Total[Transpose[FactorInteger[n, GaussianIntegers -> True]][[2]]], {n, 100}]