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 A326815 #18 Aug 22 2021 05:56:29
%S A326815 1,1,1,0,1,1,1,-2,0,1,1,0,1,1,1,-5,1,0,1,0,1,1,1,-2,0,1,-2,0,1,1,1,-9,
%T A326815 1,1,1,0,1,1,1,-2,1,1,1,0,0,1,1,-5,0,0,1,0,1,-2,1,-2,1,1,1,0,1,1,0,
%U A326815 -14,1,1,1,0,1,1,1,0,1,1,0,0,1,1,1,-5,-5,1,1,0,1
%N A326815 Dirichlet g.f.: zeta(s)^3 * Product_{p prime} (1 - 2 * p^(-s)).
%C A326815 Inverse Moebius transform applied twice to A076479 (unitary Moebius function).
%H A326815 Antti Karttunen, <a href="/A326815/b326815.txt">Table of n, a(n) for n = 1..16384</a>
%H A326815 Antti Karttunen, <a href="/A326815/a326815.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%H A326815 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A326815 a(n) = Sum_{d|n} (-1)^omega(n/d) * tau(d), where omega = A001221 and tau = A000005.
%F A326815 a(n) = Sum_{d|n} tau_3(n/d) * mu(d) * 2^omega(d), where tau_3 = A007425 and mu = A008683.
%F A326815 Multiplicative with a(p^e) = (e+1)*(2-e)/2 = A080956(e). - _Amiram Eldar_, Oct 26 2020
%t A326815 Table[Sum[(-1)^PrimeNu[n/d] DivisorSigma[0, d], {d, Divisors[n]}], {n, 1, 85}]
%t A326815 f[p_, e_] := (e + 1)*(2 - e)/2; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Oct 26 2020 *)
%o A326815 (PARI) A326815(n) = sumdiv(n,d,((-1)^omega(n/d))*numdiv(d)); \\ _Antti Karttunen_, Nov 17 2019
%o A326815 (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - 2*X)/(1 - X)^3)[n], ", ")) \\ _Vaclav Kotesovec_, Aug 22 2021
%Y A326815 Cf. A000005, A001221, A005117 (positions of 1's), A007425, A008683, A038109 (positions of 0's), A046951, A076479, A080956, A326814.
%K A326815 sign,mult,easy
%O A326815 1,8
%A A326815 _Ilya Gutkovskiy_, Oct 19 2019