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 A333493 #7 Mar 24 2020 14:05:21
%S A333493 1,1,-2,13,-9,28,-20,109,-11,151,-54,256,-77,442,48,877,-135,757,-170,
%T A333493 1363,103,1816,-252,2080,-59,3043,-38,3982,-405,2878,-464,7021,273,
%U A333493 6937,390,6817,-665,9748,388,11059,-819,8407,-902,16348,219,17458,-1080,16672,-167
%N A333493 a(n) = Sum_{k=1..n} (-1)^(k+1) * lcm(n,k) / gcd(n,k).
%H A333493 <a href="/index/Ga#gcd">Index entries for sequences related to gcd's</a>
%H A333493 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F A333493 If n odd, a(n) = (1/2) * n * Sum_{d|n} Sum_{j|d} (-1)^(j + 1) * mu(d/j) * (n + d) / j^2.
%F A333493 If n even, a(n) = (1/2) * n^2 * Sum_{d|n} Sum_{j|d} (-1)^(j + 1) * mu(d/j) * (n + d) / (d * j^2).
%t A333493 Table[Sum[(-1)^(k + 1) LCM[n, k]/GCD[n, k], {k, 1, n}], {n, 1, 49}]
%o A333493 (PARI) a(n) = sum(k=1, n, (-1)^(k+1)*lcm(n, k)/gcd(n, k)); \\ _Michel Marcus_, Mar 24 2020
%Y A333493 Alternating row sums of A051537.
%Y A333493 Cf. A056789, A089913, A199084, A199806.
%K A333493 sign
%O A333493 1,3
%A A333493 _Ilya Gutkovskiy_, Mar 24 2020