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 A349914 #11 Dec 10 2021 22:55:39
%S A349914 2,0,0,1,0,8,0,1,16,12,0,4,0,16,48,1,0,10,0,6,64,24,0,4,36,28,40,8,0,
%T A349914 0,0,1,96,36,96,13,0,40,112,6,0,0,0,12,60,48,0,4,64,26,144,14,0,40,
%U A349914 144,8,160,60,0,24,0,64,80,1,168,0,0,18,192,0,0,13,0,76,104,20,192,0,0,6,121,84,0,32,216,88,240
%N A349914 Sum of A000593 (the sum of odd divisors function) and its Dirichlet inverse.
%H A349914 Antti Karttunen, <a href="/A349914/b349914.txt">Table of n, a(n) for n = 1..16384</a>
%F A349914 a(n) = A000593(n) + A327278(n).
%F A349914 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A000593(d) * A327278(n/d).
%F A349914 a(4*n) = A000593(n).
%t A349914 f1[p_,e_] := If[p==2, 1, (p^(e+1)-1)/(p-1)]; f2[p_, e_] := If[p == 2, -Boole[e == 1], Which[e == 1, -p - 1, e == 2, p, e > 2, 0]]; a[1] = 2; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) + Times @@ f2 @@@ f; Array[a, 100] (* _Amiram Eldar_, Dec 08 2021 *)
%o A349914 (PARI)
%o A349914 A000593(n) = sigma(n>>valuation(n, 2));
%o A349914 A327278(n) = sumdiv(n,d,if(d%2,d*moebius(d)*moebius(n/d),0));
%o A349914 A349914(n) = (A000593(n)+A327278(n));
%Y A349914 Cf. A000593 (also a quadrisection of this sequence), A327278.
%Y A349914 Cf. also A349913, A349916.
%K A349914 nonn
%O A349914 1,1
%A A349914 _Antti Karttunen_, Dec 08 2021