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Search: id:A102531
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| A102531 |
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Real part of absolute Gaussian perfect numbers, in order of increasing magnitude. See A102532 for the imaginary part. |
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+0
5
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| 3, 15, 6, 19, 111, 91, 159, 72, 472, 904, 2584, 1616, 999, 4328, 702, 4424, 7048, 7328, 2474, 9352, 7144
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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An absolute Gaussian perfect number z satisfies abs(sigma(z)-z) = abs(z), where sigma(z) is sum of the divisors of z, as defined by Spira for Gaussian integers.
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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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EXAMPLE
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For z=3+7i, we have sigma(z)-z = 7+3i, which has the same magnitude as z.
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MATHEMATICA
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lst={}; nn=1000; Do[z=a+b*I; If[Abs[z]<=nn && Abs[(DivisorSigma[1, z]-z)] == Abs[z], AppendTo[lst, {Abs[z]^2, z}]], {a, nn}, {b, nn}]; Re[Transpose[Sort[lst]][[2]]]
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CROSSREFS
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Cf. A102506 and A102507 (Gaussian multiperfect numbers). See also A101366, A101367.
Sequence in context: A012881 A066832 A102777 this_sequence A135546 A138006 A099476
Adjacent sequences: A102528 A102529 A102530 this_sequence A102532 A102533 A102534
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 13 2005
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