%I A119966
%S A119966 1,2,6,28,220,2565,45846,1268622,55336336,3876385680
%N A119966 The n-almost primeth recurrence: a(0) = 1, a(n) = n-almostprime(a(n-1)).
%e A119966 a(0)=1, a(1) is the first prime 2, a(2) is the second semiprime 6, a(3) 
               is the sixth 3-almost prime 28, etc.
%t A119966 AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], 
               Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ 
               Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, 
               i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]]]]]; (* Eric W.Weisstein 
               (eww(AT)wolfram.com) Feb 07 2006 *)
%t A119966 AlmostPrime[k_Integer,n] = Block[{e = Floor[ Log[2, n] + 1], a, b}, a 
               = 2^e; Do[b = 2^p; While[AlmostPrimePi[k, a] < n, a = a + b]; a = 
               a - b/2, {p, e, 0, -1}]; a + b/2];
%Y A119966 Cf. A007097, A105999, A119965.
%Y A119966 Sequence in context: A093657 A006117 A118025 this_sequence A002047 A126340 
               A136639
%Y A119966 Adjacent sequences: A119963 A119964 A119965 this_sequence A119967 A119968 
               A119969
%K A119966 nonn
%O A119966 0,2
%A A119966 Jonathan Vos Post (jvospost3(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), 
               May 31 2006