A332319 Imaginary part of Gaussian norm-multiply-perfect numbers, in order of increasing norm.

0, 1, 3, 1, 2, 5, 4, 10, 16, 14, 2, 18, 22, 26, 18, 20, 41, 1, 36, 48, 24, 12, 65, 70, 24, 64, 82, 88, 45, 15, 100, 20, 94, 100, 130, 132, 84, 120, 184, 30, 148, 108, 32, 216, 192, 48, 228, 212, 51, 24, 252, 188, 60, 282, 283, 209, 312, 216, 198, 440, 102, 490

Offset: 1

Author

Amiram Eldar, Feb 09 2020

Keywords

• nonn

Comments

See A332318 (the corresponding real parts) for the definition of Gaussian norm-multiply-perfect numbers.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..182

Crossrefs

Cf. A000396, A007691, A100884, A100885, A100889, A100890, A102506, A102507, A102531, A102532, A103228, A103229, A103230, A332318.

Programs

Mathematica

csigma[z_] := DivisorSigma[1, z, GaussianIntegers -> True]; normultPerf[z_] := Divisible[Abs[csigma[z]]^2, Abs[z]^2]; seq = {}; max = 10^2; Do[z = a + b*I; If[Abs[z] <= max && normultPerf[z], AppendTo[seq, {Abs[z]^2, z}]], {a, 1, max}, {b, 0, max}]; Im[Transpose[Sort[seq]][[2]]] (* after T. D. Noe at A102532 *)