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 A370898 #7 Mar 05 2024 11:51:52
%S A370898 1,-2,2,-3,3,-9,-1,-10,0,-18,-6,-26,-12,-36,-12,-29,-11,-41,-21,-51,
%T A370898 -19,-55,-31,-67,-41,-83,-55,-95,-65,-137,-105,-138,-90,-144,-96,-146,
%U A370898 -108,-168,-112,-166,-124,-220,-176,-236,-176,-248,-200,-268,-218,-296,-224,-294,-240,-324,-252,-324,-244,-334,-274,-394
%N A370898 Partial alternating sums of the sum of unitary divisors function (A034448).
%H A370898 Amiram Eldar, <a href="/A370898/b370898.txt">Table of n, a(n) for n = 1..10000</a>
%H A370898 László Tóth, <a href="https://www.emis.de/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1.
%F A370898 a(n) = Sum_{k=1..n} (-1)^(k+1) * A034448(k).
%F A370898 a(n) = -c * n^2 + O(n * log(n)^(5/3)), where c = Pi^2/(84*zeta(3)) = 0.0977451984014... (Tóth, 2017).
%t A370898 usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); usigma[1] = 1; Accumulate[Array[(-1)^(# + 1) * usigma[#] &, 100]]
%o A370898 (PARI) usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]);}
%o A370898 lista(kmax) = {my(s = 0); for(k = 1, kmax, s += (-1)^(k+1) * usigma(k); print1(s, ", "))};
%Y A370898 Cf. A002117, A034448, A064609.
%Y A370898 Similar sequences: A068762, A068773, A307704, A357817, A362028.
%K A370898 sign,easy
%O A370898 1,2
%A A370898 _Amiram Eldar_, Mar 05 2024