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A050614 Products of distinct terms of A001566: a(n) = Product_{i=0..floor(log_2(n+1))} L(2^(i+1))^bit(n,i).

%I A050614 #24 Jan 05 2025 19:51:36
%S A050614 1,3,7,21,47,141,329,987,2207,6621,15449,46347,103729,311187,726103,
%T A050614 2178309,4870847,14612541,34095929,102287787,228929809,686789427,
%U A050614 1602508663,4807525989,10749959329,32249877987,75249715303
%N A050614 Products of distinct terms of A001566: a(n) = Product_{i=0..floor(log_2(n+1))} L(2^(i+1))^bit(n,i).
%C A050614 Each subset a(0..(2^k)-1) gives all the divisors of F(2^(k+1)) up to k=4 (F_32) and after that a subset of such divisors. E.g., the terms a(0)-a(7) are the divisors of F_16 = 987 (A018760).
%H A050614 Robert Price, <a href="/A050614/b050614.txt">Table of n, a(n) for n = 0..200</a>
%H A050614 A. Karttunen, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-1/quartkarttunen01_2004.pdf">On Pascal's Triangle Modulo 2 in Fibonacci Representation</a>, Fibonacci Quarterly, 42 (2004), 38-46.
%F A050614 a(n) = Sum_{k=0..n} A127872(n,k)*Fibonacci(2*k+1), see A000045 and A001519. - _Philippe Deléham_, Aug 30 2007
%p A050614 [seq(A050614(n),n=0..30)]; A050614 := n -> product('luc(2^(i+1))^bit_i(n,i)','i'=0..floor_log_2(n+1));
%t A050614 Table[k = Floor[Log[2, n + 1]]; Product[j = 2^(i + 1); l = Fibonacci[j + 1] + Fibonacci[j - 1]; If[BitAnd[2^i, n] == 0, b = 0, b = 1]; l^b, {i, 0, k}], {n, 0, 200}] (* _Robert Price_, Feb 13 2017 *)
%Y A050614 Bisection of A075149 and A050613 (see there for the other Maple procedures), subset of A062877. Cf. also A050615.
%K A050614 nonn
%O A050614 0,2
%A A050614 _Antti Karttunen_, Dec 02 1999