

A102531


Real part of absolute Gaussian perfect numbers, in order of increasing magnitude.


7



3, 15, 6, 19, 111, 91, 159, 72, 472, 904, 2584, 1616, 999, 4328, 702, 4424, 7048, 7328, 2474, 9352, 7144, 7240, 5117, 739, 6327, 15128, 13168, 1263, 14280, 3224, 21704, 15160, 21992, 14044, 23132, 9135, 23656, 24614, 7272, 15464, 9040, 28424, 30956, 14728, 32399
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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

Amiram Eldar, Table of n, a(n) for n = 1..76
R. Spira, The Complex Sum Of Divisors, American Mathematical Monthly, 1961 Vol. 68, pp. 120124.


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

See A102532 for the imaginary part.
Cf. A102506 and A102507 (Gaussian multiperfect numbers). See also A101366, A101367.
Sequence in context: A248031 A066832 A102777 * A135546 A138006 A335696
Adjacent sequences: A102528 A102529 A102530 * A102532 A102533 A102534


KEYWORD

nonn


AUTHOR

T. D. Noe, Jan 13 2005


EXTENSIONS

a(22)a(45) from Amiram Eldar, Feb 10 2020


STATUS

approved



