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 A348953 #14 Aug 21 2025 09:55:55
%S A348953 0,1,-1,1,-1,3,-1,-1,-1,3,-1,2,-1,3,-4,-1,-1,6,-1,3,-4,3,-1,-2,-1,3,
%T A348953 -4,3,-1,11,-1,-5,-4,3,-6,6,-1,3,-4,0,-1,12,-1,3,-9,3,-1,-8,-1,8,-4,3,
%U A348953 -1,12,-6,2,-4,3,-1,5,-1,3,-11,-5,-6,12,-1,3,-4,15,-1,0,-1,3,-9,3,-8,12,-1,-8
%N A348953 a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d) * d.
%H A348953 Antti Karttunen, <a href="/A348953/b348953.txt">Table of n, a(n) for n = 1..20000</a>
%F A348953 G.f.: Sum_{k>=1} k * x^(k*(k + 1)) / (1 + x^k).
%F A348953 a(n) = A037213(n) - A348608(n). - _Ridouane Oudra_, Aug 21 2025
%t A348953 Table[-DivisorSum[n, (-1)^(# + n/#) # &, # < Sqrt[n] &], {n, 1, 80}]
%t A348953 nmax = 80; CoefficientList[Series[Sum[k x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A348953 (PARI) A348953(n) = -sumdiv(n,d,if((d*d)<n,d*(-1)^(d + (n/d)),0)); \\ _Antti Karttunen_, Nov 05 2021
%Y A348953 Cf. A000593, A046897, A070039, A109506, A333810, A348608, A348951, A348952, A348954, A348955, A348956, A037213.
%K A348953 sign
%O A348953 1,6
%A A348953 _Ilya Gutkovskiy_, Nov 04 2021