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 A038063 #36 May 29 2025 01:07:48
%S A038063 2,-3,2,-3,6,-11,18,-30,56,-105,186,-335,630,-1179,2182,-4080,7710,
%T A038063 -14588,27594,-52377,99858,-190743,364722,-698870,1342176,-2581425,
%U A038063 4971008,-9586395,18512790,-35792449,69273666,-134215680,260300986
%N A038063 Product_{k>=1}1/(1 - x^k)^a(k) = 1 + 2x.
%C A038063 Apart from initial terms, exponents in expansion of A065472 as a product zeta(n)^(-a(n)).
%H A038063 Seiichi Manyama, <a href="/A038063/b038063.txt">Table of n, a(n) for n = 1..3000</a>
%H A038063 G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%H A038063 N. J. A. Sloane, <a href="/transforms.txt">Euler transform</a>.
%F A038063 a(n) = (1/n) * Sum_{d divides n} (-1)^(d+1)*moebius(n/d)*2^d. - _Vladeta Jovovic_, Sep 06 2002
%F A038063 G.f.: Sum_{n>=1} moebius(n)*log(1 + 2*x^n)/n, where moebius(n) = A008683(n). - _Paul D. Hanna_, Oct 13 2010
%F A038063 For n == 0, 1, 3 (mod 4), a(n) = (-1)^(n+1)*A001037(n), which for n>1 also equals (-1)^(n+1)*A059966(n) = (-1)^(n+1)*A060477(n).
%F A038063 For n == 2 (mod 4), a(n) = -(A001037(n) + A001037(n/2)). - _George Beck_ and _Max Alekseyev_, May 23 2016
%F A038063 a(n) ~ -(-1)^n * 2^n / n. - _Vaclav Kotesovec_, Jun 12 2018
%t A038063 a[n_] := DivisorSum[n, (-1)^(#+1) * MoebiusMu[n/#]*2^# &] / n; Array[a, 33] (* _Amiram Eldar_, May 29 2025 *)
%o A038063 (PARI) {a(n)=polcoeff(sum(k=1,n,moebius(k)/k*log(1+2*x^k+x*O(x^n))),n)} \\ _Paul D. Hanna_, Oct 13 2010
%Y A038063 Cf. A001037, A008683, A038064, A038065, A038066, A038067, A038068, A038069, A038070, A059966, A060477, A065472.
%K A038063 sign
%O A038063 1,1
%A A038063 _Christian G. Bower_, Jan 04 1999