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 A349568 #12 Jan 09 2024 13:19:26
%S A349568 1,-1,-5,-16,-65,-187,-665,-1984,-6260,-18895,-58025,-174016,-527345,
%T A349568 -1583407,-4765595,-14307568,-42981185,-128980852,-387158345,
%U A349568 -1161657760,-3485726195,-10458022927,-31376865305,-94134053296,-282412754000,-847252941535,-2541798630320,-7625456893096,-22876524019505,-68629821114805
%N A349568 Dirichlet convolution of A011782 [2^(n-1)] with A349453 (Dirichlet inverse of A133494, 3^(n-1)).
%C A349568 Dirichlet convolution of this sequence with A034754 produces A034738.
%H A349568 Antti Karttunen, <a href="/A349568/b349568.txt">Table of n, a(n) for n = 1..1001</a>
%F A349568 a(n) = Sum_{d|n} 2^(d-1) * A349453(n/d).
%t A349568 s[1] = 1; s[n_] := s[n] = -DivisorSum[n, s[#] * 3^(n/# - 1) &, # < n &]; a[n_] := DivisorSum[n, 2^(# - 1) * s[n/#] &]; Array[a, 30] (* _Amiram Eldar_, Nov 22 2021 *)
%o A349568 (PARI)
%o A349568 A133494(n) = max(1, 3^(n-1));
%o A349568 memoA349453 = Map();
%o A349568 A349453(n) = if(1==n,1,my(v); if(mapisdefined(memoA349453,n,&v), v, v = -sumdiv(n,d,if(d<n,A133494(n/d)*A349453(d),0)); mapput(memoA349453,n,v); (v)));
%o A349568 A349568(n) = sumdiv(n,d,(2^(d-1)) * A349453(n/d));
%Y A349568 Cf. A011782, A133494, A349453, A349567 (Dirichlet inverse).
%Y A349568 Cf. also A034738, A034754, A349564, A349566, A349570.
%K A349568 sign
%O A349568 1,3
%A A349568 _Antti Karttunen_, Nov 22 2021