%I
%S 2,15,255,5865,170085,9014505,1661569239,117971415969,494390700895,
%T 42163217429333,2571956263189313,551363902358334637
%N a(n) is the smallest "cyclic" integer, k, that has exactly n prime factors.
%C The cyclic numbers are given in A003277.
%C a(n) = k if k = p_1*p_2*...*p_n where the p_i are distinct primes and no p_j1 is divisible by any p_i and k is the smallest such integer.
%e The prime factorizations for the first 12 terms are:
%e 2
%e 3, 5
%e 3, 5, 17
%e 3, 5, 17, 23
%e 3, 5, 17, 23, 29
%e 3, 5, 17, 23, 29, 53
%e 3, 11, 17, 29, 41, 47, 53
%e 3, 11, 17, 29, 41, 47, 53, 71
%e 5, 7, 13, 17, 19, 23, 37, 59, 67
%e 7, 11, 13, 17, 19, 31, 37, 41, 47, 59
%e 7, 11, 13, 17, 19, 31, 37, 41, 47, 59, 61
%e 11, 13, 17, 19, 29, 31, 37, 41, 43, 47, 61, 71
%t (* about 45 seconds on laptop computer *)
%t f[list_] := Boole[Map[Apply[Divisible, #] &,
%t Level[Table[Table[{list[[i]]  1, list[[j]]}, {i, j + 1, Length[list]}], {j,1, Length[list]  1}], {2}]]]; Prepend[Map[Apply[Times, #] &,
%t Table[First[Select[Subsets[Table[Prime[n], {n, 2, 18}], {k}],
%t Total[f[#]] == 0 &]], {k, 2, 10}]], 2]
%Y Cf. A003277.
%K nonn,more
%O 1,1
%A _Geoffrey Critzer_, Nov 28 2015
