A102531 Real part of absolute Gaussian perfect numbers, in order of increasing magnitude.

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

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. 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

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