

A333620


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


4



1, 2, 3, 4, 12, 28, 33, 68, 104, 126, 130, 143, 147, 220, 231, 248, 297, 336, 390, 391, 408, 416, 429, 442, 518, 575, 741, 752, 779, 812, 825, 1161, 1170, 1197, 1295, 1323, 1364, 1440, 1462, 1566, 1652, 1677, 1680, 1692, 1701, 1720, 1806, 1817, 1872, 1909, 2210
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..51.


EXAMPLE

4 is a term since its divisors are {1, 2, 4}, their dual Zeckendorf representations (A104326) are {1, 10, 101}, and their sum of sums of digits is 1 + (1 + 0) + (1 + 0 + 1) = 4 which is a divisor of 4.


MATHEMATICA

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[10^3], Divisible[#, dualZeckDivDigSum[#]] &]


CROSSREFS

Cf. A093705, A104326, A112310, A328212, A333617, A333618, A333619.
Sequence in context: A037397 A168047 A236371 * A173446 A053350 A165302
Adjacent sequences: A333617 A333618 A333619 * A333621 A333622 A333623


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Mar 29 2020


STATUS

approved



