%I #5 Jun 24 2022 08:30:39

%S 1,1,5,21,89,345,1405,5501,22033,87649,350405,1398981,5596345,

%T 22373561,89492141,357930301,1431711857,5726679153,22906712645,

%U 91626189381,366504720137,1466016390873,5864065352173,23456251396589,93825005578001,375299982311441,1501199928316661

%N a(1) = 1; a(n+1) = Sum_{d|n} 4^(n/d - 1) * a(d).

%F G.f.: x * ( 1 + Sum_{n>=1} a(n) * x^n / (1 - 4 * x^n) ).

%F a(n) ~ 4^(n-1) / 3.

%t a[1] = 1; a[n_] := a[n] = Sum[4^((n - 1)/d - 1) a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 27}]

%Y Cf. A003238, A351405, A355116.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Jun 19 2022