%I #27 Jan 30 2013 15:17:45
%S 2,3,9,10,27,28,30,81,84,88,90,100,104,243,252,264,270,272,280,300,
%T 304,312,729,736,756,784,792,810,816,840,880,900,912,928,936,992,1000,
%U 1040,2187,2208,2268,2352,2368,2376,2430,2448,2464,2520,2624
%N Let T(n,k) be the n-th k-almost prime. Then a(n) = T(n,k) such that k is minimal and for all l>0, T(n,k+l) > 2^l * T(n,k).
%C If one writes the k-almost primes in rows (one row for each k), one observes that there exists a P_{k_0}(n) such that P_{k_0+1}(n) = 2P_{k_0}(n) and for each k>=k_0, P_{k+1}(n)=2P_{k}(n). Then a(n) = P_{k_0}(n). In other words in the columns the values double from row k_0 on. - Peter Pein (petsie(AT)dordos.net), Mar 16 2007
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Almost_prime">k-almost prime numbers</a>.
%t a[n_] := Module[{p = Prime[Range[n]], pal}, pal = Transpose /@ Partition[NestList[Take[Union[Flatten[Outer[Times, #1, p]]], Length[#1]] &, p, n], 2, 1]; Complement @@ Transpose[Cases[pal, {k_, kk_} /; kk == 2*k, {2}]]] ; a[50] (* Peter Pein, Nov 10 2007 *)
%Y Cf. A000040, A001358, A014612, A014613, A014614, A078840.
%K nonn
%O 1,1
%A Yury V. Shlapak (shlapak(AT)imp.kiev.ua), Aug 04 2005
%E Edited by _Max Alekseyev_, Mar 16 2007
%E More terms from Peter Pein, Mar 16 2007