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

1,2

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

Links

Table of n, a(n) for n=1..75.

Eric Weisstein's World of Mathematics, Gaussian Integer.

Formula

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

Example

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.

Crossrefs

Cf. A000005, A062327.

Sequence in context: A367832 A307869 A016695 * A245262 A092314 A237750

Adjacent sequences: A125268 A125269 A125270 * A125272 A125273 A125274

Keyword

easy,nonn

Author

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

Status

approved