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A125271 Number of Gaussian integer divisors of n (having positive real part). 0
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 (list; graph; refs; listen; history; text; internal format)
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) = count(gauss_divisors(n))

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.

Sequence in context: A143370 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

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Last modified June 5 15:37 EDT 2020. Contains 334852 sequences. (Running on oeis4.)