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A333619
Numbers that are divisible by the total number of 1's in the Zeckendorf representations of all their divisors (A300837).
5
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
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[#]] &]
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 29 2020
STATUS
approved