A239627 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Cf. A001221, A001222 (integer factorizations).

Cf. A078458, A086275 (Gaussian factorizations).

Cf. A239626 (Gaussian factorization including units).

Sequence in context: A337557 A186333 A272917 * A101933 A117127 A278148

Adjacent sequences: A239624 A239625 A239626 * A239628 A239629 A239630

KEYWORD

nonn

AUTHOR

T. D. Noe, Mar 31 2014

STATUS

approved