A102924 Real part of Gaussian amicable numbers in order of increasing magnitude. See A102925 for the imaginary part.

-1105, -1895, -2639, -3235, -3433, -3970, -4694, -3549, -766, -4478, -6880, 5356, -6468, 8008, 4232, -8547

Offset

1,1

Comments

For a Gaussian integer z, let the sum of the proper divisors be denoted by s(z) = sigma(z)-z, where sigma(z) is sum of the divisors of z, as defined by Spira for Gaussian integers. Then z is an amicable Gaussian number if z and s(z) are different and z = s(s(z)). The smallest Gaussian amicable number in the first quadrant is 8008+3960i.

Links

Table of n, a(n) for n=1..16.

R. Spira, The Complex Sum Of Divisors, American Mathematical Monthly, 1961 Vol. 68, pp. 120-124.

Eric Weisstein's World of Mathematics, Amicable Pair

Example

For z=-1105+1020i, we have s(z)=-2639-1228i and s(s(z))=z.

Mathematica

s[z_Complex] := DivisorSigma[1, z]-z; nn=10000; lst={}; Do[d=a^2+b^2; If[d<nn^2, z=a+b*I; Do[If[s[s[z]]==z, AppendTo[lst, {d, z}]]; z=z*I, {4}]], {a, nn}, {b, nn}]; Re[Transpose[Sort[lst]][[2]]]

Crossrefs

Cf. A102506 (Gaussian multiperfect numbers), A102531 (absolute Gaussian perfect numbers).

Sequence in context: A281877 A159781 A264498 * A214017 A083738 A265237

Adjacent sequences: A102921 A102922 A102923 * A102925 A102926 A102927

Keyword

sign,more

Author

T. D. Noe, Jan 19 2005

Status

approved