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A344441 a(n) = A061020(n) + abs(A061020(n)).

%I A344441 #12 May 26 2021 02:34:20
%S A344441 2,0,0,6,0,4,0,0,14,8,0,0,0,12,16,22,0,0,0,0,24,20,0,20,42,24,0,0,0,0,
%T A344441 0,0,40,32,48,42,0,36,48,40,0,0,0,0,0,44,0,0,86,0,64,0,0,40,80,60,72,
%U A344441 56,0,48,0,60,0,86,96,0,0,0,88,0,0,0,0,72,0,0,120,0,0,0,122,80,0,72,128,84,112,100,0,56,144
%N A344441 a(n) = A061020(n) + abs(A061020(n)).
%C A344441 a(k) = 0 for k in A026424. - _David A. Corneth_, May 23 2021
%H A344441 Antti Karttunen, <a href="/A344441/b344441.txt">Table of n, a(n) for n = 1..20000</a>
%F A344441 a(n) = A061020(n) + A206369(n) = A061020(n) + abs(A061020(n)).
%F A344441 a(n) = A344440(n) - A344439(n).
%t A344441 With[{nn = 91}, Map[# + Abs[#] &, Drop[CoefficientList[Series[Sum[LiouvilleLambda[k] k x^k/(1 - x^k), {k, 1, #}], {x, 0, #}], x], 1] &[nn]]] (* _Michael De Vlieger_, May 24 2021, after _Jean-François Alcover_ at A061020 *)
%o A344441 (PARI)
%o A344441 A061020(n) = {my(f=factorint(n)); prod(k=1, #f[, 2], ((-f[k, 1])^(f[k, 2]+1)-1)/(-f[k, 1]-1))};
%o A344441 A344441(n) = { my(u=A061020(n)); (u+abs(u)); };
%Y A344441 Cf. A026424, A061020, A206369, A344439, A344441.
%K A344441 nonn
%O A344441 1,1
%A A344441 _Antti Karttunen_, May 23 2021