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A084296 Triangle: number of distinct prime factors in n-th primorial numbers when n prime factors first appears and in n-1 subsequent integers after.

%I A084296 #9 Jun 23 2017 21:24:23
%S A084296 1,2,1,3,1,1,4,1,2,2,5,1,2,2,3,6,2,2,3,2,2,7,3,2,3,3,2,4,8,2,3,2,4,2,
%T A084296 3,2,9,2,3,3,3,2,4,3,4,10,3,3,2,2,2,4,3,3,2,11,1,4,3,2,4,5,4,3,3,4,12,
%U A084296 3,3,4,2,3,6,2,3,5,4,3,13,3,4,2,3,3,3,3,3,3,6,2,4,14,2,3,2,4,5,4,5,3,3,6,4
%N A084296 Triangle: number of distinct prime factors in n-th primorial numbers when n prime factors first appears and in n-1 subsequent integers after.
%C A084296 Omega-values(=A001221) in the subsequent neighborhood of radius n, for primorial numbers are usually neither all distinct or all equal items as it is required in A068069, A045983 sequences.
%e A084296 n-th row of table consists of n numbers A001221[A002110(n+j)], j=0...n-1:
%e A084296 1,
%e A084296 2,1,
%e A084296 3,1,1,
%e A084296 4,1,2,2,
%e A084296 5,1,2,2,3,
%e A084296 6,2,2,3,2,2,
%e A084296 7,3,2,3,3,2,4,
%e A084296 Rows starts with n at indices which are central polygonal numbers:a[A000124(n)]=n; rows ends at a[A000217(n)] terms, at triangular number indices.
%t A084296 lf[x_] := Length[FactorInteger[x]] q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]] Flatten[Table[Table[lf[q[n]+j], {j, 0, n-1}], {n, 1, 20}], 1]
%Y A084296 Cf. A001221, A002110, A068069, A045983, A000217, A000124.
%K A084296 nonn,tabl
%O A084296 1,2
%A A084296 _Labos Elemer_, May 27 2003