A125271 Number of Gaussian integer divisors of n (having positive real part).

1, 4, 2, 7, 6, 8, 2, 10, 3, 20, 2, 14, 6, 8, 12, 13, 6, 12, 2, 34, 4, 8, 2, 20, 15, 20, 4, 14, 6, 40, 2, 16, 4, 20, 12, 21, 6, 8, 12, 48, 6, 16, 2, 14, 18, 8, 2, 26, 3, 48, 12, 34, 6, 16, 12, 20, 4, 20, 2, 68, 6, 8, 6, 19, 28, 16, 2, 34, 4, 40, 2, 30, 6, 20, 30

Offset: 1

Author

Mitch Cervinka (puritan(AT)toast.net), Jan 16 2007

Keywords

• easy
• nonn

Comments

To avoid the redundancy of counting the negatives of the divisors, we consider only divisors having a positive real part.

The usual method of counting complex divisors is to exclude associates. For example, although 1+i and 1-i both divide 2, one is just -i times the other. This sequence counts each first-quadrant complex divisor twice. Sequence A062327 counts those complex divisors only once. - T. D. Noe, Feb 21 2007

Examples

			a(5) = 6 because 5 is divisible by the Gaussian integers {1, 1-2i, 1+2i, 2-i, 2+i, 5}, which is 6 divisors in all.
		

Links

• Eric Weisstein's World of Mathematics, Gaussian Integer.

Crossrefs

Cf. A000005, A062327.

Formula

a(n) = 2*A062327(n) - A000005(n). - T. D. Noe, Feb 21 2007