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