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 A378434 #6 Nov 26 2024 17:14:17
%S A378434 1,-3,-4,5,-6,12,-8,-9,9,18,-12,-20,-14,24,24,16,-18,-27,-20,-30,32,
%T A378434 36,-24,36,20,42,-24,-40,-30,-72,-32,-30,48,54,48,48,-38,60,56,54,-42,
%U A378434 -96,-44,-60,-54,72,-48,-64,35,-60,72,-70,-54,72,72,72,80,90,-60,120,-62,96,-72,56,84,-144,-68,-90,96,-144,-72,-90
%N A378434 Arithmetic mean between the Dirichlet inverses of {sum of unitary divisors} and {sum of squarefree divisors}.
%C A378434 Arithmetic mean between A158523 and A178450.
%C A378434 Apparently differs from A378433 at positions given by A048111: 16, 32, 36, 48, 64, 72, 80, 81, 96, ...
%H A378434 Antti Karttunen, <a href="/A378434/b378434.txt">Table of n, a(n) for n = 1..20000</a>
%F A378434 a(n) = (1/2) * (A158523(n)+A178450(n)).
%o A378434 (PARI)
%o A378434 A158523(n) = { my(f = factor(n)); prod(i = 1, #f~, (-1)^f[i, 2]*(f[i, 1]+1)*f[i, 1]^(f[i, 2]-1)); }; \\ From A158523
%o A378434 A178450(n) = { my(f=factor(n)); prod(i=1, #f~, if(!(f[i,2]%2), 2*(f[i, 1]^(f[i, 2]/2)), -(1+f[i,1])*(f[i, 1]^((f[i, 2]-1)/2)))); };
%o A378434 A378434(n) = ((A158523(n)+A178450(n))/2);
%Y A378434 Cf. A034448, A048111, A048250, A158523, A178450, A325973, A378433, A378435 (Dirichlet inverse).
%K A378434 sign
%O A378434 1,2
%A A378434 _Antti Karttunen_, Nov 26 2024