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 A331108 Zeckendorf-infinitary perfect numbers: numbers k such that A331107(k) = 2*k. 1
 6, 60, 90, 3024, 133056, 1330560, 6879600, 28828800, 302702400, 698544000, 11763214848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No more terms below 4*10^10. LINKS Table of n, a(n) for n=1..11. EXAMPLE 6 is a term since A331107(6) = 12 = 2*6. 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 *) CROSSREFS Cf. A007357, A038182, A074849, A097464, A331107. Sequence in context: A334406 A322486 A323757 * A324707 A007357 A327158 Adjacent sequences: A331105 A331106 A331107 * A331109 A331110 A331111 KEYWORD nonn,more AUTHOR Amiram Eldar, Jan 09 2020 STATUS approved

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Last modified September 21 17:02 EDT 2023. Contains 365503 sequences. (Running on oeis4.)