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 A349567 #10 Nov 25 2021 12:15:48
%S A349567 1,1,5,17,65,197,665,2017,6285,19025,58025,174565,527345,1584737,
%T A349567 4766245,14311841,42981185,128995317,387158345,1161697825,3485732845,
%U A349567 10458138977,31376865305,94134428213,282412758225,847253996225,2541798693045,7625460083185,22876524019505,68629830861205,205890058352825,617671220125537
%N A349567 Dirichlet convolution of A133494 [3^(n-1)] with A349452 (Dirichlet inverse of A011782, 2^(n-1)).
%C A349567 Dirichlet convolution of this sequence with A034738 produces A034754.
%H A349567 Antti Karttunen, <a href="/A349567/b349567.txt">Table of n, a(n) for n = 1..1001</a>
%F A349567 a(n) = Sum_{d|n} 3^(d-1) * A349452(n/d).
%t A349567 s[1] = 1; s[n_] := s[n] = -DivisorSum[n, s[#] * 2^(n/# - 1) &, # < n &]; a[n_] := DivisorSum[n, 3^(# - 1) * s[n/#] &]; Array[a, 32] (* _Amiram Eldar_, Nov 22 2021 *)
%o A349567 (PARI)
%o A349567 A011782(n) = (2^(n-1));
%o A349567 memoA349452 = Map();
%o A349567 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 A349567 A349567(n) = sumdiv(n,d,(3^(d-1)) * A349452(n/d));
%Y A349567 Cf. A011782, A133494, A349452, A349568 (Dirichlet inverse).
%Y A349567 Cf. also A034738, A034754, A349563, A349565, A349569.
%K A349567 nonn
%O A349567 1,3
%A A349567 _Antti Karttunen_, Nov 22 2021