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

1,2

Links

Table of n, a(n) for n=1..35.

Formula

a(1) = 1; a(n) = Sum_{d|n, d<n} 2^(n/d-1)*a(d).

a(n) ~ 2^(n-1). - Vaclav Kotesovec, Oct 16 2019

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}]

Crossrefs

Cf. A011782, A050354, A050369, A054599, A074206.

Sequence in context: A053636 A181135 A054440 * A303819 A074646 A097001

Adjacent sequences: A308073 A308074 A308075 * A308077 A308078 A308079

Keyword

nonn

Author

Ilya Gutkovskiy, May 11 2019

Status

approved