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 A378433 #6 Nov 26 2024 15:21:39
%S A378433 1,-3,-4,5,-6,12,-8,-9,9,18,-12,-20,-14,24,24,15,-18,-27,-20,-30,32,
%T A378433 36,-24,36,20,42,-24,-40,-30,-72,-32,-27,48,54,48,42,-38,60,56,54,-42,
%U A378433 -96,-44,-60,-54,72,-48,-60,35,-60,72,-70,-54,72,72,72,80,90,-60,120,-62,96,-72,45,84,-144,-68,-90,96,-144,-72,-72
%N A378433 Dirichlet inverse of A325973, where A325973 is the arithmetic mean of {sum of unitary divisors} and {sum of squarefree divisors}.
%C A378433 Apparently differs from A378434 at positions given by A048111: 16, 32, 36, 48, 64, 72, 80, 81, 96, ...
%H A378433 Antti Karttunen, <a href="/A378433/b378433.txt">Table of n, a(n) for n = 1..20000</a>
%F A378433 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A325973(n/d) * a(d).
%o A378433 (PARI)
%o A378433 A325973(n) = (1/2)*sumdiv(n, d, d*(issquarefree(d) + (1==gcd(d, n/d))));
%o A378433 memoA378433 = Map();
%o A378433 A378433(n) = if(1==n,1,my(v); if(mapisdefined(memoA378433,n,&v), v, v = -sumdiv(n,d,if(d<n,A325973(n/d)*A378433(d),0)); mapput(memoA378433,n,v); (v)));
%Y A378433 Cf. A034448, A048111, A048250, A325973, A378434.
%K A378433 sign
%O A378433 1,2
%A A378433 _Antti Karttunen_, Nov 26 2024