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A214343 a(n) is the smallest integer j such that the numbers of prime factors (counting multiplicity) in j, j+1, ... , j+n-1 are the full set {1,2,...,n}.

%I A214343 #16 Jul 15 2012 12:50:55
%S A214343 2,3,6,15,77,726,6318,189375,755968,871593371,33714015615
%N A214343 a(n) is the smallest integer j such that the numbers of prime factors (counting multiplicity) in j, j+1, ... , j+n-1 are the full set {1,2,...,n}.
%C A214343 Next term a(10) > 5*10^7. _Joerg Arndt_, Jul 14 2012
%e A214343 a(4)=15 because 15 has two prime factors, 16 has four, 17 has one and 18 has three (and 15 is the smallest number with this property).
%e A214343 a(5) = 77 because 77, 78, 79, 80 and 81 have 2, 3, 1, 5 and 4 prime factors.
%p A214343 A214343 := proc(n)
%p A214343     refs := {seq(i,i=1..n)} ;
%p A214343     for j from 1 do
%p A214343         pf := {} ;
%p A214343         for k from 0 to n-1 do
%p A214343             pf := pf union {numtheory[bigomega](j+k)} ;
%p A214343             if nops(pf) < k+1 then
%p A214343                 break;
%p A214343             end if;
%p A214343         end do:
%p A214343         if pf = refs then
%p A214343             return j;
%p A214343         end if;
%p A214343     end do:
%p A214343 end proc: # _R. J. Mathar_, Jul 13 2012
%t A214343 f[n_] := f[n] = FactorInteger[n][[All, 2]] // Total;
%t A214343 n = 1;
%t A214343 i = 2;
%t A214343 While[True,
%t A214343   While[Union[Table[f[j], {j, i, i + n - 1}]] != Range[n],
%t A214343    i += 1; f[i] =.
%t A214343    ];
%t A214343   Print[i]; n += 1;
%t A214343   ];
%Y A214343 Cf. A072875, A001222.
%K A214343 nonn
%O A214343 1,1
%A A214343 _Jake Foster_, Jul 13 2012
%E A214343 a(10)-a(11) from _Donovan Johnson_, Jul 15 2012