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.
%I A309840 #13 Jul 14 2024 15:15:27
%S A309840 1,2,3,6,5,10,15,30,8,16,24,48,40,80,120,240,13,26,39,78,65,130,195,
%T A309840 390,104,208,312,624,520,1040,1560,3120,21,42,63,126,105,210,315,630,
%U A309840 168,336,504,1008,840,1680,2520,5040,273,546,819,1638,1365,2730,4095,8190
%N A309840 If n = Sum (2^e_k) then a(n) = Product (Fibonacci(e_k + 3)).
%H A309840 Michael De Vlieger, <a href="/A309840/b309840.txt">Table of n, a(n) for n = 0..16384</a>
%H A309840 Michael De Vlieger, <a href="/A309840/a309840.png">Fan style binary tree</a> showing a(n) for n = 0..2^14, showing primes in red, perfect prime powers in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue and magenta, where magenta additionally represents powerful numbers that are not perfect prime powers and bright green represents primorials.
%F A309840 G.f.: Product_{k>=0} (1 + Fibonacci(k + 3) * x^(2^k)).
%F A309840 a(0) = 1; a(n) = Fibonacci(floor(log_2(n)) + 3) * a(n - 2^floor(log_2(n))).
%F A309840 a(2^(k-2)-1) = A003266(k).
%e A309840 23 = 2^0 + 2^1 + 2^2 + 2^4 so a(23) = Fibonacci(3) * Fibonacci(4) * Fibonacci(5) * Fibonacci(7) = 390.
%t A309840 nmax = 55; CoefficientList[Series[Product[(1 + Fibonacci[k + 3] x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%t A309840 a[0] = 1; a[n_] := Fibonacci[Floor[Log[2, n]] + 3] a[n - 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 55}]
%o A309840 (PARI) a(n)={vecprod([fibonacci(k+2) | k<-Vec(select(b->b, Vecrev(digits(n, 2)), 1))])} \\ _Andrew Howroyd_, Aug 19 2019
%Y A309840 Cf. A000045, A003266, A019565, A022290, A029930, A121663, A160009.
%K A309840 nonn
%O A309840 0,2
%A A309840 _Ilya Gutkovskiy_, Aug 19 2019