A345182 - OEIS

%I #11 Dec 14 2021 00:23:21

%S 1,0,1,1,1,2,1,2,2,2,1,5,1,2,3,4,1,6,1,5,3,2,1,12,2,2,4,5,1,10,1,8,3,

%T 2,3,18,1,2,3,12,1,10,1,5,8,2,1,28,2,6,3,5,1,16,3,12,3,2,1,31,1,2,8,

%U 16,3,10,1,5,3,10,1,50,1,2,8,5,3,10,1,28,8,2,1,31,3,2,3,12,1,36

%N a(1) = 1, a(2) = 0; a(n) = Sum_{d|n, d < n} a(d).

%H Antti Karttunen, <a href="/A345182/b345182.txt">Table of n, a(n) for n = 1..20000</a>

%F G.f. A(x) satisfies: A(x) = x - x^2 + A(x^2) + A(x^3) + A(x^4) + ...

%F a(n) = A074206(n) if n is odd, otherwise a(n) = A074206(n) - A074206(n/2).

%t a[1] = 1; a[2] = 0; a[n_] := a[n] = Sum[If[d < n, a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 90}]

%t nmax = 90; A[_] = 0; Do[A[x_] = x - x^2 + Sum[A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

%Y Cf. A022825 (partial sums), A074206, A167865, A320224, A345138, A345141.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Jun 10 2021