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%I #8 Oct 07 2019 19:18:33
%S 1,2,3,4,5,6,8,9,10,12,13,14,15,16,18,21,22,24,26,27,28,30,32,34,35,
%T 36,39,40,42,44,45,48,50,52,55,56,57,58,60,63,64,65,66,68,69,70,72,75,
%U 76,78,80,81,84,85,89,90,92,93,94,95,96,99,100,102,104,105,108
%N Weak-Fibonacci-Niven numbers: numbers divisible by the number of terms in at least one representation as a sum of distinct Fibonacci numbers.
%C The Fibonacci numbers F(1) = F(2) = 1 can be used at most once in the representation.
%C Grundman proved that there are infinitely many runs of 6 consecutive weak-Fibonacci-Niven numbers by showing that if m = F(240k) + F(14) + F(9) for k >= 1, then m, m+1, ... m+5 are 6 consecutive weak-Fibonacci-Niven numbers.
%H Helen G. Grundman, <a href="https://www.fq.math.ca/Papers1/45-3/grundman.pdf">Consecutive Zeckendorf-Niven and lazy-Fibonacci-Niven numbers</a>, Fibonacci Quarterly, Vol. 45, No. 3 (2007), pp. 272-276.
%e 6 is in the sequence since it can be represented as the sum of 2 Fibonacci numbers, 1 + 5, and 2 is a divisor of 6.
%t m = 10; v = Array[Fibonacci, m, 2]; vm = v[[-1]]; seq = {}; Do[s = Subsets[v, 2^m, {k}]; If[(sum = Total @@ s) <= vm && Divisible[sum, Length @@ s], AppendTo[seq, sum]] , {k, 2, 2^m}]; Union @ seq
%Y Supersequence of A328208 and A328212.
%Y Cf. A000045, A005349.
%K nonn
%O 1,2
%A _Amiram Eldar_, Oct 07 2019
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