A372626 - OEIS

%I #6 May 11 2024 21:51:30

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

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

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

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

%F G.f.: Sum_{k>=1} (-1)^(k + 1) * a(k) * x^(k^2) / (1 + x^k).

%t a[1] = 1; a[n_] := a[n] = DivisorSum[n, (-1)^(n/# + 1) a[#] &, # <= Sqrt[n] &]; Table[a[n], {n, 80}]

%o (PARI) a(n) = if (n==1, 1, sumdiv(n, d, if (d^2 <= n, (-1)^(n/d+1)*a(d)))); \\ _Michel Marcus_, May 09 2024

%Y Cf. A308077, A337135, A348660.

%K sign

%O 1,6

%A _Ilya Gutkovskiy_, May 07 2024