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 A102531 Real part of absolute Gaussian perfect numbers, in order of increasing magnitude. See A102532 for the imaginary part. 4
 3, 15, 6, 19, 111, 91, 159, 72, 472, 904, 2584, 1616, 999, 4328, 702, 4424, 7048, 7328, 2474, 9352, 7144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS R. Spira, The Complex Sum Of Divisors, American Mathematical Monthly, 1961 Vol. 68, pp. 120-124. EXAMPLE For z=3+7i, we have sigma(z)-z = 7+3i, which has the same magnitude as z. MATHEMATICA 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]]] CROSSREFS Cf. A102506 and A102507 (Gaussian multiperfect numbers). See also A101366, A101367. Sequence in context: A248031 A066832 A102777 * A135546 A138006 A256557 Adjacent sequences:  A102528 A102529 A102530 * A102532 A102533 A102534 KEYWORD nonn,more AUTHOR T. D. Noe, Jan 13 2005 STATUS approved

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Last modified August 21 05:40 EDT 2019. Contains 326162 sequences. (Running on oeis4.)