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A338639 a(0) = 1; for n > 0, a(n) = -Sum_{d|n, d < n} a(d - 1).

%I A338639 #7 Aug 14 2021 04:22:10
%S A338639 1,0,-1,-1,-1,-1,0,-1,0,0,0,-1,2,-1,-1,1,1,-1,1,-1,1,0,-1,-1,4,0,-3,0,
%T A338639 1,-1,3,-1,0,0,-2,0,4,-1,-2,-2,3,-1,1,-1,0,2,0,-1,4,-1,-4,-1,-2,-1,5,
%U A338639 0,2,-1,-2,-1,7,-1,-4,-1,1,-2,1,-1,-1,1,3,-1,6,-1,-5,-2,0,-1,1,-1,4
%N A338639 a(0) = 1; for n > 0, a(n) = -Sum_{d|n, d < n} a(d - 1).
%H A338639 Seiichi Manyama, <a href="/A338639/b338639.txt">Table of n, a(n) for n = 0..10000</a>
%F A338639 G.f. A(x) satisfies: A(x) = 1 - x^2 * A(x^2) - x^3 * A(x^3) - x^4 * A(x^4) - ...
%t A338639 a[0] = 1; a[n_] := a[n] = -DivisorSum[n, a[# - 1] &, # < n &]; Table[a[n], {n, 0, 80}]
%t A338639 nmax = 80; A[_] = 0; Do[A[x_] = 1 - Sum[x^k A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A338639 Cf. A167865, A281487, A308077, A343371.
%K A338639 sign
%O A338639 0,13
%A A338639 _Ilya Gutkovskiy_, Nov 05 2020