%I #12 Nov 26 2021 08:54:25
%S 2,0,0,4,0,8,0,16,4,8,0,16,0,8,8,52,0,24,0,16,8,8,0,40,4,8,24,16,0,0,
%T 0,160,8,8,8,56,0,8,8,40,0,0,0,16,24,8,0,112,4,40,8,16,0,80,8,40,8,8,
%U 0,16,0,8,24,484,8,0,0,16,8,0,0,152,0,8,40,16,8,0,0,112,112,8,0,16,8,8,8,40,0,16,8,16
%N a(n) = A349355(n) + A349356(n).
%H Antti Karttunen, <a href="/A349357/b349357.txt">Table of n, a(n) for n = 1..20000</a>
%F a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A349355(d) * A349356(n/d). [As the sequences are Dirichlet inverses of each other]
%t f1[p_, e_] := -2*(p - 1)^(e - 1); f2[p_, e_] := 2*(p + 1)^(e - 1); a[1] = 2; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) + Times @@ f2 @@@ f; Array[a, 100] (* _Amiram Eldar_, Nov 16 2021 *)
%o (PARI) A349357(n) = (A349355(n)+A349356(n)); \\ Needs also code from A349355 and A349356.
%Y Cf. A003958, A003959, A063441, A097945, A349355, A349356.
%K nonn
%O 1,1
%A _Antti Karttunen_, Nov 16 2021