cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A333619 #12 Oct 12 2023 06:20:06
%S A333619 1,2,4,10,15,18,20,25,44,55,56,63,70,78,80,96,108,126,128,190,275,324,
%T A333619 338,341,416,442,451,484,494,517,520,550,637,682,720,726,736,760,780,
%U A333619 781,803,816,845,946,990,1088,1111,1113,1199,1235,1239,1311,1426,1441
%N A333619 Numbers that are divisible by the total number of 1's in the Zeckendorf representations of all their divisors (A300837).
%H A333619 Amiram Eldar, <a href="/A333619/b333619.txt">Table of n, a(n) for n = 1..10000</a>
%e A333619 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.
%t A333619 zeckDigSum[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5] * # + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]];
%t A333619 zeckDivDigSum[n_] := DivisorSum[n, zeckDigSum[#] &];
%t A333619 Select[Range[10^3], Divisible[#, zeckDivDigSum[#]] &]
%Y A333619 Cf. A007895, A014417, A093705, A300837, A328208, A333617, A333620.
%K A333619 nonn,base
%O A333619 1,2
%A A333619 _Amiram Eldar_, Mar 29 2020