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A348660 a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(n/d + 1) * d.

%I A348660 #11 Dec 14 2021 12:10:54
%S A348660 1,-1,1,-3,1,1,1,-3,4,1,1,-6,1,1,4,-7,1,-2,1,1,4,1,1,-10,6,1,4,1,1,-7,
%T A348660 1,-7,4,1,6,-8,1,1,4,-12,1,4,1,1,9,1,1,-16,8,-4,4,1,1,4,6,-14,4,1,1,
%U A348660 -13,1,1,11,-15,6,4,1,1,4,-11,1,-8,1,1,9,1,8,4,1,-20
%N A348660 a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(n/d + 1) * d.
%H A348660 Antti Karttunen, <a href="/A348660/b348660.txt">Table of n, a(n) for n = 1..20000</a>
%F A348660 G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^(k^2) / (1 + x^k).
%t A348660 Table[DivisorSum[n, (-1)^(n/# + 1) # &, # <= Sqrt[n] &], {n, 1, 80}]
%t A348660 nmax = 80; CoefficientList[Series[Sum[(-1)^(k + 1) k x^(k^2)/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A348660 (PARI) a(n) = sumdiv(n, d, if(sqr(d) <= n, (-1)^(n/d + 1)*d, 0)); \\ _Michel Marcus_, Oct 28 2021, corrected by _Antti Karttunen_, Dec 14 2021
%Y A348660 Cf. A000593, A066839, A109506, A333782, A348608.
%K A348660 sign
%O A348660 1,4
%A A348660 _Ilya Gutkovskiy_, Oct 28 2021