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 A349565 #11 Nov 25 2021 12:15:31
%S A349565 1,-1,-2,-3,-11,-16,-51,-93,-214,-419,-935,-1812,-3863,-7649,-15698,
%T A349565 -31443,-63939,-127676,-257963,-516037,-1037298,-2076547,-4165647,
%U A349565 -8335716,-16702015,-33421217,-66911078,-133875827,-267921227,-535987784,-1072395555,-2145208557,-4291436930,-8584038291,-17170640199,-34344407256
%N A349565 Dirichlet convolution of Fibonacci numbers with A349452 (Dirichlet inverse of A011782, 2^(n-1)).
%C A349565 Dirichlet convolution of this sequence with A034738 produces A034748.
%H A349565 Antti Karttunen, <a href="/A349565/b349565.txt">Table of n, a(n) for n = 1..1001</a>
%F A349565 a(n) = Sum_{d|n} A000045(d) * A349452(n/d).
%t A349565 s[1] = 1; s[n_] := s[n] = -DivisorSum[n, s[#] * 2^(n/# - 1) &, # < n &]; a[n_] := DivisorSum[n, Fibonacci[#] * s[n/#] &]; Array[a, 36] (* _Amiram Eldar_, Nov 22 2021 *)
%o A349565 (PARI)
%o A349565 A011782(n) = (2^(n-1));
%o A349565 memoA349452 = Map();
%o A349565 A349452(n) = if(1==n,1,my(v); if(mapisdefined(memoA349452,n,&v), v, v = -sumdiv(n,d,if(d<n,A011782(n/d)*A349452(d),0)); mapput(memoA349452,n,v); (v)));
%o A349565 A349565(n) = sumdiv(n,d,fibonacci(d)*A349452(n/d));
%Y A349565 Cf. A000045, A011782, A349452, A349566 (Dirichlet inverse).
%Y A349565 Cf. also A034738, A034748, A349563, A349567, A349569.
%K A349565 sign
%O A349565 1,3
%A A349565 _Antti Karttunen_, Nov 22 2021