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
KEYWORD
nonn
AUTHOR
T. D. Noe, Jan 13 2005
EXTENSIONS
a(22)-a(45) from Amiram Eldar, Feb 10 2020
STATUS
approved