%I #8 Sep 11 2017 19:47:46
%S 1,1,2,1,1,2,1,1,4,2,2,2,1,1,2,1,1,4,2,2,2,1,1,2,1,1,8,4,4,6,2,2,6,2,
%T 2,4,2,2,2,1,1,2,1,1,4,2,2,2,1,1,2,1,1,8,4,4,6,2,2,6,2,2,4,2,2,2,1,1,
%U 2,1,1,4,2,2,2,1,1,2,1,1,16,8,8,12,4,4,12,4,4,12,6,6,6,2,2,6,2,2,12,6,6,6,2,2,6
%N Filter based on runlengths of 0-digits in base-3 expansion of n: a(n) = A278222(A291770(n)).
%H Antti Karttunen, <a href="/A291771/b291771.txt">Table of n, a(n) for n = 1..59049</a>
%F a(n) = A278222(A291770(n)).
%t f[n_, i_, x_] := Which[n == 0, x, EvenQ@ n, f[n/2, i + 1, x], True, f[(n - 1)/2, i, x Prime@ i]]; Array[If[# == 1, 1, Times @@ MapIndexed[Prime[First[#2]]^#1 &, Sort[FactorInteger[#][[All, -1]], Greater]]] &@ f[FromDigits[IntegerDigits[#, 3] /. k_ /; k < 3 :> If[k == 0, 1, 0], 2], 1, 1] &, 96] (* _Michael De Vlieger_, Sep 11 2017 *)
%Y Cf. A007089, A077267, A278222, A291770, A290091, A290092, A290093, A290094.
%K nonn,base
%O 1,3
%A _Antti Karttunen_, Sep 11 2017