A331108 Zeckendorf-infinitary perfect numbers: numbers k such that A331107(k) = 2*k.

6, 60, 90, 3024, 133056, 1330560, 6879600, 28828800, 302702400, 698544000, 11763214848

Offset: 1

Author

Amiram Eldar, Jan 09 2020

Keywords

• nonn
• more

Comments

No more terms below 4*10^10.

Examples

			6 is a term since A331107(6) = 12 = 2*6.
		

Crossrefs

Cf. A007357, A038182, A074849, A097464, A331107.

Programs

Mathematica

fb[n_] := Block[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k--]; Fibonacci[1 + Position[Reverse@fr, ?(# == 1 &)]]]; f[p, e_] := p^fb[e]; zsigma[1] = 1; zsigma[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) + 1); zPerfectQ[n_] := zsigma[n] == 2 n; Select[Range[10^4], zPerfectQ] (* after Robert G. Wilson v at A014417 *)