A333619 Numbers that are divisible by the total number of 1's in the Zeckendorf representations of all their divisors (A300837).

1, 2, 4, 10, 15, 18, 20, 25, 44, 55, 56, 63, 70, 78, 80, 96, 108, 126, 128, 190, 275, 324, 338, 341, 416, 442, 451, 484, 494, 517, 520, 550, 637, 682, 720, 726, 736, 760, 780, 781, 803, 816, 845, 946, 990, 1088, 1111, 1113, 1199, 1235, 1239, 1311, 1426, 1441

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

4 is a term since its divisors are {1, 2, 4}, their Zeckendorf representations (A014417) 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

zeckDigSum[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5] * # + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]];
zeckDivDigSum[n_] := DivisorSum[n, zeckDigSum[#] &];
Select[Range[10^3], Divisible[#, zeckDivDigSum[#]] &]

Crossrefs

Cf. A007895, A014417, A093705, A300837, A328208, A333617, A333620.

Sequence in context: A080149 A217134 A351927 * A128513 A048200 A058201

Adjacent sequences: A333616 A333617 A333618 * A333620 A333621 A333622

Keyword

nonn,base

Author

Amiram Eldar, Mar 29 2020

Status

approved