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 A369100 #12 Jan 18 2025 19:31:43
%S A369100 1,-1,3,-2,3,-3,3,-2,6,-3,3,-6,3,-3,9,-1,3,-6,3,-6,9,-3,3,-6,6,-3,10,
%T A369100 -6,3,-9,3,1,9,-3,9,-12,3,-3,9,-6,3,-9,3,-6,18,-3,3,-3,6,-6,9,-6,3,
%U A369100 -10,9,-6,9,-3,3,-18,3,-3,18,4,9,-9,3,-6,9,-9,3,-12,3,-3,18
%N A369100 Dirichlet g.f.: zeta(s)^3 * (1 - 2^(1-s))^2.
%H A369100 Antti Karttunen, <a href="/A369100/b369100.txt">Table of n, a(n) for n = 1..20000</a>
%F A369100 Sum_{k=1..n} a(k) ~ n * log(2)^2.
%F A369100 Multiplicative with a(2^e) = (e^2-5*e+2)/2, and a(p^e) = (e+1)*(e+2)/2 for an odd prime p. - _Amiram Eldar_, Jan 13 2024
%t A369100 Table[Sum[Sum[-(-1)^d, {d, Divisors[k]}]*(-1)^(n/k+1), {k, Divisors[n]}], {n, 1, 100}]
%t A369100 f[p_, e_] := (e + 1)*(e + 2)/2; f[2, e_] := (e^2 - 5*e + 2)/2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jan 13 2024 *)
%o A369100 (PARI) a(n) = {my(f = factor(n), p, e); prod(i = 1, #f~, p = f[i,1]; e=f[i,2]; if(p == 2, (e^2-5*e+2)/2, (e+1)*(e+2)/2));} \\ _Amiram Eldar_, Jan 13 2024
%Y A369100 Cf. A007425, A048272, A288571.
%K A369100 sign,mult
%O A369100 1,3
%A A369100 _Vaclav Kotesovec_, Jan 13 2024