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 A378528 #8 Dec 01 2024 13:41:05
%S A378528 1,-1,-1,0,-1,1,-1,0,-1,1,-1,-1,-1,1,0,-1,-1,1,-1,-1,0,1,-1,1,-1,1,1,
%T A378528 -1,-1,0,-1,1,0,1,0,1,-1,1,0,1,-1,0,-1,-1,2,1,-1,1,-1,1,0,-1,-1,-1,0,
%U A378528 1,0,1,-1,2,-1,1,2,0,0,0,-1,-1,0,0,-1,-1,-1,1,2,-1,0,0,-1,1,0,1,-1,2,0,1,0,1,-1,-2,0,-1,0,1,0,-1,-1,1,2,1,-1,0,-1,1,2
%N A378528 Dirichlet inverse of A378444.
%H A378528 Antti Karttunen, <a href="/A378528/b378528.txt">Table of n, a(n) for n = 1..20000</a>
%F A378528 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A378444(n/d) * a(d).
%F A378528 a(n) = Sum_{d|n} A000010(n/d)*A378527(d).
%F A378528 a(n) = Sum_{d|n} A008683(n/d)*A369974(d).
%o A378528 (PARI)
%o A378528 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A378528 A369001(n) = !(A083345(n)%2);
%o A378528 A378444(n) = sumdiv(n,d,A369001(d));
%o A378528 memoA378528 = Map();
%o A378528 A378528(n) = if(1==n,1,my(v); if(mapisdefined(memoA378528,n,&v), v, v = -sumdiv(n,d,if(d<n,A378444(n/d)*A378528(d),0)); mapput(memoA378528,n,v); (v)));
%Y A378528 Cf. A000010, A008683, A378444, A378527.
%Y A378528 Möbius transform of A369974.
%K A378528 sign
%O A378528 1,45
%A A378528 _Antti Karttunen_, Dec 01 2024