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 A174273 #17 Nov 13 2022 08:39:33
%S A174273 1,1,2,2,2,2,2,2,3,2,2,4,2,2,4,3,2,3,2,4,4,2,2,4,3,2,4,4,2,4,2,3,4,2,
%T A174273 4,6,2,2,4,4,2,4,2,4,6,2,2,6,3,3,4,4,2,4,4,4,4,2,2,8,2,2,6,4,4,4,2,4,
%U A174273 4,4,2,6,2,2,6,4,4,4,2,6,5,2,2,8,4,2,4,4,2,6,4,4,4,2,4,6,2,3,6,6,2,4,2,4,8
%N A174273 Inverse Moebius transform of A035263.
%H A174273 Antti Karttunen, <a href="/A174273/b174273.txt">Table of n, a(n) for n = 1..65537</a>
%F A174273 a(1) = 1, a(2n) = -a(n) + A000005(2n), a(2n+1) = sigma(2n+1) (A000203).
%F A174273 Dirichlet g.f.: 2^s*(zeta(s))^2/(2^s+1). - _R. J. Mathar_, Feb 06 2011
%F A174273 From _Amiram Eldar_, Nov 13 2022: (Start)
%F A174273 Multiplicative with s(2^e) = e+1-floor((e+1)/2) and a(p^e) = e+1 if p>2.
%F A174273 Sum_{k=1..n} a(k) ~ (2/3)*n*log(n) + (2/3)*(2*gamma - 1 + log(2)/2)*n, where gamma is Euler's constant (A001620). (End)
%t A174273 f[p_, e_] := e + 1 - If[p == 2, Floor[(e + 1)/2], 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 13 2022 *)
%o A174273 (PARI) A174273(n) = sumdiv(n,d,(valuation(2*d,2)%2)); \\ _Antti Karttunen_, Sep 27 2018
%o A174273 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,2]+1-if(f[i,1] == 2, floor((f[i,2]+1)/2), 0)); } \\ _Amiram Eldar_, Nov 13 2022
%Y A174273 Cf. A000005, A000035, A000203, A001511, A001620, A035263.
%K A174273 nonn,mult
%O A174273 1,3
%A A174273 _Ralf Stephan_, Nov 27 2010
%E A174273 More terms from _Antti Karttunen_, Sep 27 2018