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A364006 Wythoff-Niven numbers: numbers that are divisible by the number of 1's in their Wythoff representation.

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%I A364006 #11 Apr 27 2025 03:23:00
%S A364006 1,3,4,6,7,8,10,12,15,18,20,21,24,26,28,32,35,39,40,42,45,47,51,52,54,
%T A364006 55,56,60,68,72,76,80,84,86,88,90,91,98,100,102,105,117,120,123,125,
%U A364006 135,136,138,141,143,144,156,164,168,172,174,176,178,180,188,192
%N A364006 Wythoff-Niven numbers: numbers that are divisible by the number of 1's in their Wythoff representation.
%C A364006 Numbers k such that A135818(k) | k.
%C A364006 Includes all the positive even-indexed Fibonacci numbers (A001906), since the Wythoff representation of Fibonacci(2*n), for n >= 1, is 1 followed by n-1 0's.
%H A364006 Amiram Eldar, <a href="/A364006/b364006.txt">Table of n, a(n) for n = 1..10000</a>
%t A364006 wnQ[n_] := (s = Total[w[n]]) > 0 && Divisible[n, s] (* using the function w[n] from A364005 *)
%Y A364006 Cf. A135818, A189921.
%Y A364006 Subsequences: A364007, A364008, A364009.
%Y A364006 Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719, A352089, A352107, A352320, A352508.
%K A364006 nonn,base
%O A364006 1,2
%A A364006 _Amiram Eldar_, Jul 01 2023