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%I #8 Apr 17 2021 19:36:57
%S 1,1,0,0,-1,0,-1,0,-1,0,0,0,-1,0,0,1,-1,0,0,0,0,1,-1,0,-1,1,0,1,0,0,0,
%T 0,-2,0,0,2,0,0,-1,1,0,0,0,0,-2,2,0,0,-2,1,1,1,-1,0,0,1,-1,0,-1,0,0,0,
%U -1,2,-2,2,0,0,0,1,1,0,-2,0,-1,2,-1,1,0,0,-2,1,-1,0,-1,2,-1,0,-2,0,3
%N a(n) = 1 - Sum_{d|n, d < n} a(d - 1).
%F G.f. A(x) satisfies: A(x) = 1 / (1 - x) - x^2 * A(x^2) - x^3 * A(x^3) - x^4 * A(x^4) - ...
%t a[n_] := a[n] = 1 - Sum[If[d < n, a[d - 1], 0], {d, Divisors[n]}]; Table[a[n], {n, 0, 90}]
%t nmax = 90; A[_] = 0; Do[A[x_] = 1/(1 - x) - Sum[x^k A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) //Normal, nmax + 1]; CoefficientList[A[x], x]
%o (Python)
%o from functools import lru_cache
%o from sympy import divisors
%o @lru_cache(maxsize=None)
%o def A343493(n): return 1-sum(A343493(d-1) for d in divisors(n) if d < n) # _Chai Wah Wu_, Apr 17 2021
%Y Cf. A167865, A281487, A338639, A343371.
%K sign
%O 0,33
%A _Ilya Gutkovskiy_, Apr 17 2021