A333621 Numbers that are divisible by the total number of 1's in both the Zeckendorf and the dual Zeckendorf representations of all their divisors (A300837 and A333618).

1, 2, 4, 126, 416, 442, 3025, 4588, 9243, 10428, 11900, 15070, 18176, 19436, 20532, 26956, 28582, 32108, 33028, 35278, 35929, 37634, 47678, 50386, 61952, 69254, 74578, 88984, 93534, 95120, 96334, 100326, 102297, 142894, 144039, 145768, 147664, 152817, 163125, 183002

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Example

126 is a term since A300837(126) = 21 and A333618(126) = 7 are both divisors of 126.

Mathematica

zeckDigSum[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5] * # + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]];
zeckDivDigSum[n_] := DivisorSum[n, zeckDigSum[#] &];
fibTerms[n_] := Module[{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--]; fr];
dualZeckSum[n_] := Module[{v = fibTerms[n]}, nv = Length[v]; i = 1; While[i <= nv - 2, If[v[[i]] == 1 && v[[i + 1]] == 0 && v[[i + 2]] == 0, v[[i]] = 0; v[[i + 1]] = 1; v[[i + 2]] = 1; If[i > 2, i -= 3]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, 0, Total[v[[i[[1, 1]] ;; -1]]]]];
dualZeckDivDigSum[n_] := DivisorSum[n, dualZeckSum[#] &];
Select[Range[10^4], Divisible[#, zeckDivDigSum[#]] && Divisible[#, dualZeckDivDigSum[#]] &]

Crossrefs

Intersection of A333619 and A333620.

Cf. A007895, A112310, A300837, A330711, A333617, A333618.

Sequence in context: A006314 A326204 A259381 * A009595 A018493 A046035

Adjacent sequences: A333618 A333619 A333620 * A333622 A333623 A333624

Keyword

nonn,base

Author

Amiram Eldar, Mar 29 2020

Status

approved