%I #10 Dec 14 2021 12:10:40

%S 0,1,-1,1,-1,0,-1,2,-1,0,-1,3,-1,0,-2,2,-1,1,-1,1,-2,0,-1,4,-1,0,-2,1,

%T -1,2,-1,3,-2,0,-2,2,-1,0,-2,4,-1,0,-1,1,-3,0,-1,5,-1,1,-2,1,-1,0,-2,

%U 4,-2,0,-1,4,-1,0,-3,3,-2,0,-1,1,-2,2,-1,4,-1,0,-3,1,-2,0,-1,5

%N a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(n/d).

%H Antti Karttunen, <a href="/A348951/b348951.txt">Table of n, a(n) for n = 1..20000</a>

%F G.f.: Sum_{k>=1} (-1)^(k + 1) * x^(k*(k + 1)) / (1 + x^k).

%t Table[DivisorSum[n, (-1)^(n/#) &, # < Sqrt[n] &], {n, 1, 80}]

%t nmax = 80; CoefficientList[Series[Sum[(-1)^(k + 1) x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%o (PARI) A348951(n) = sumdiv(n,d,if((d*d)<n,(-1)^(n/d),0)); \\ _Antti Karttunen_, Nov 05 2021

%Y Cf. A048272, A056924, A113652, A228441, A333809, A348515, A348952, A348953, A348954, A348955, A348956.

%K sign

%O 1,8

%A _Ilya Gutkovskiy_, Nov 04 2021