A308076 G.f. A(x) satisfies: A(x) = x + 2*A(x^2) + 4*A(x^3) + 8*A(x^4) + ... + 2^(k-1)*A(x^k) + ...
1, 2, 4, 12, 16, 48, 64, 168, 272, 576, 1024, 2288, 4096, 8448, 16512, 33456, 65536, 132448, 262144, 526784, 1049088, 2101248, 4194304, 8399232, 16777472, 33570816, 67110976, 134252288, 268435456, 536942336, 1073741824, 2147618976, 4294975488, 8590196736, 17179871232
Offset: 1
Keywords
Programs
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Mathematica
terms = 35; A[] = 0; Do[A[x] = x + Sum[2^(k - 1) A[x^k], {k, 2, terms}] + O[x]^(terms + 1) //Normal, terms + 1]; Rest[CoefficientList[A[x], x]] a[n_] := If[n == 1, n, Sum[If[d < n, 2^(n/d - 1) a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 35}]
Formula
a(1) = 1; a(n) = Sum_{d|n, d
a(n) ~ 2^(n-1). - Vaclav Kotesovec, Oct 16 2019