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 A365800 #9 Oct 05 2023 18:17:11
%S A365800 1,0,-1,0,0,-1,0,0,1,-1,0,0,0,0,-1,0,0,2,0,0,-1,0,0,0,0,0,-1,-1,0,2,0,
%T A365800 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-3,-1,0,0,0,0,2,0,0,2,0,
%U A365800 0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,2,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,1,0,0,0,0,-1
%N A365800 Dirichlet inverse of the characteristic function of triangular numbers (A010054).
%H A365800 Antti Karttunen, <a href="/A365800/b365800.txt">Table of n, a(n) for n = 1..101025</a>
%F A365800 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A010054(n/d) * a(d).
%o A365800 (PARI)
%o A365800 A010054(n) = issquare(8*n + 1);
%o A365800 memoA365800 = Map();
%o A365800 A365800(n) = if(1==n,1,my(v); if(mapisdefined(memoA365800,n,&v), v, v = -sumdiv(n,d,if(d<n,A010054(n/d)*A365800(d),0)); mapput(memoA365800,n,v); (v)));
%Y A365800 Cf. A000217, A010054, A365799 (parity of terms).
%Y A365800 Absolute values differ from A308264.
%K A365800 sign
%O A365800 1,18
%A A365800 _Antti Karttunen_, Oct 05 2023