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 A349355 #17 Nov 26 2021 08:16:10
%S A349355 1,-2,-2,-2,-2,4,-2,-2,-4,4,-2,4,-2,4,4,-2,-2,8,-2,4,4,4,-2,4,-8,4,-8,
%T A349355 4,-2,-8,-2,-2,4,4,4,8,-2,4,4,4,-2,-8,-2,4,8,4,-2,4,-12,16,4,4,-2,16,
%U A349355 4,4,4,4,-2,-8,-2,4,8,-2,4,-8,-2,4,4,-8,-2,8,-2,4,16,4,4,-8,-2,4,-16,4,-2,-8,4,4,4,4,-2,-16
%N A349355 Dirichlet convolution of A003958 with A063441 (Dirichlet inverse of A003959), where A003958 and A003959 are fully multiplicative with a(p) = p-1 and p+1 respectively.
%C A349355 Multiplicative because both A003958 and A063441 are.
%C A349355 In Dirichlet ring this sequence works as a kind of replacement operator which replaces the factor A003959 with factor A003958. For example, convolving this with A003968 (the Möbius transform of A003959) produces A003966, the Möbius transform of A003958.
%H A349355 Antti Karttunen, <a href="/A349355/b349355.txt">Table of n, a(n) for n = 1..20000</a>
%H A349355 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dirichlet_convolution">Dirichlet convolution</a>
%F A349355 a(n) = Sum_{d|n} A003958(n/d) * A063441(d).
%F A349355 Multiplicative with a(p^e) = -2*(p-1)^(e-1). - _Amiram Eldar_, Nov 16 2021
%t A349355 f[p_, e_] := -2*(p - 1)^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 16 2021 *)
%o A349355 (PARI)
%o A349355 A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
%o A349355 A063441(n) = (moebius(n)*sigma(n)); \\ Also Dirichlet inverse of A003959.
%o A349355 A349355(n) = sumdiv(n,d,A003958(n/d)*A063441(d));
%Y A349355 Cf. A003958, A003959, A003966, A003968, A063441, A349356 (Dirichlet inverse), A349357 (sum with it).
%Y A349355 Cf. also A349382.
%K A349355 sign,mult
%O A349355 1,2
%A A349355 _Antti Karttunen_, Nov 16 2021