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Search: id:A102924
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| A102924 |
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Real part of Gaussian amicable numbers in order of increasing magnitude. See A102925 for the imaginary part. |
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+0
2
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| -1105, -1895, -2639, -3235, -3433, -3970, -4694, -3549, -766, -4478, -6880, 5356, -6468, 8008, 4232, -8547
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For a Gaussian integer z, let the sum of the proper divisors be denoted by s(z) = sigma(z)-z, where sigma(z) is sum of the divisors of z, as defined by Spira for Gaussian integers. Then z is an amicable Gaussian number if z and s(z) are different and z = s(s(z)). The smallest Gaussian amicable number in the first quadrant is 8008+3960i.
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REFERENCES
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Robert Spira, The complex sum of divisors, Amer. Math. Monthly, Vol. 68, No. 2 (Feb. 1961), 120-124.
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LINKS
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Eric Weisstein's World of Mathematics, Amicable Pair
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EXAMPLE
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For z=-1105+1020i, we have s(z)=-2639-1228i and s(s(z))=z.
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MATHEMATICA
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s[z_Complex] := DivisorSigma[1, z]-z; nn=10000; lst={}; Do[d=a^2+b^2; If[d<nn^2, z=a+b*I; Do[If[s[s[z]]==z, AppendTo[lst, {d, z}]]; z=z*I, {4}]], {a, nn}, {b, nn}]; Re[Transpose[Sort[lst]][[2]]]
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CROSSREFS
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Cf. A102506 (Gaussian multiperfect numbers), A102531 (absolute Gaussian perfect numbers).
Sequence in context: A052155 A097102 A159781 this_sequence A083738 A157376 A066163
Adjacent sequences: A102921 A102922 A102923 this_sequence A102925 A102926 A102927
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KEYWORD
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sign
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 19 2005
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