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Search: id:A125271
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| A125271 |
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Number of Gaussian integer divisors of n (having positive real part). |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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 (noe(AT)sspectra.com), Feb 21 2007
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LINKS
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Eric Weisstein's World of Mathematics, "Gaussian Integer"
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FORMULA
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a(n) = count(gauss_divisors(n))
a(n)=2*A062327(n)-A000005(n) - T. D. Noe (noe(AT)sspectra.com), Feb 21 2007
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000005.
Sequence in context: A002560 A124908 A016695 this_sequence A092314 A110841 A128226
Adjacent sequences: A125268 A125269 A125270 this_sequence A125272 A125273 A125274
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KEYWORD
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easy,nonn
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AUTHOR
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Mitch Cervinka (puritan(AT)toast.net), Jan 16 2007
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